a. Write in your own words a definition of a complex numbers and Modulusof the complex number. Support your answers with examples. (4 marks) b.Find the modulus of + mi (10 marks) c. Write the complex number 2 = ((2+ m) + 3i)in polar form (13 marks) 100+m

The reflectyed point Rx is given as 6 , 3

The distance would have to be solved for first

This is the distance between the point P and the vertical line x = 2.

The distance d =  |(-2) - 2|

= |-4|

= 4

Next we have to take the point P o the other side of the line x = 2 this is the point that has the same distance

We will solve for the new coordinate

2 + 4

= 6

Hence the reflectyed point Rx is given as 6 , 3

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The integral ∫[0,6] 1/x dx is divergent, An integral is said to be divergent if it does not have a finite value.

The given integral is:

[tex]∫[0,6] 1/x dx[/tex]

We know that the integral of 1/x is ln(x), and the antiderivative of ln(x) is xln(x) - x.

So, applying the limits of integration, we get:

[tex]∫[0,6] 1/x dx = ln(x)|[0,6] = ln(6) - ln(0)[/tex]

The natural logarithm of zero is unclear, so the indispensably isn't characterized at x = 0. In this manner, the indispensability is unique.

An integral is said to be divergent in the event that it does not have limited esteem. In other words, on the off chance that the fundamentally does not meet a genuine number, it is said to be unique.

There are a few reasons why a fundamentally may be unique. A few common reasons incorporate:

The integrand gets to be unbounded at a few points inside the limits of integration.

The integrand does not approach zero as the constraint of integration approaches boundlessness.

The limits of integration are interminable, and the integrand does not merge to a limited esteem as the limits approach interminability.

When an indispensably is disparate, it implies that the zone beneath the bend is interminable or does not exist.

This could have imperative suggestions in ranges such as material science and designing, where integrands are utilized to calculate amounts such as work, energy, and a liquid stream. 

Thus, the answer is (b) Divergent. 

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The graph is attached.

Given is a triangle ABC, we need to find its coordinates if it is reflected over y = -x,

The rule of reflection over y = -x is,

(x, y) = (-x, -y)

So,

A = (-5, -4)

B = (1, -4)

C = (-1, -5)

After reflection,

A' = (5, 4)

B' = (-1, 4)

C' = (1, 5)

Hence the points after reflection are A' = (5, 4), B' = (-1, 4) and C' = (1, 5)

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Answer:

  y = 4 is line parallel to x-axis. In that line, each point's y-co-ordinate is 4.

To determine if the given subset is a subspace, verify that it satisfies the following conditions:
  a. It contains the zero vector.
  b. It is closed under vector addition.
  c. It is closed under scalar multiplication.

let's first define the terms:

1. Vector space: A collection of vectors that follow certain rules, such as closure under addition and scalar multiplication.

2. Subset: A set containing elements that are also elements of another set, called the superset.

3. Subspace: A subset of a vector space that is also a vector space by itself, following the same rules as the superset.

Now, you have not provided specific sets to analyze, but I can give you a general approach:

1. Identify the given set and check if it belongs to a known vector space (e.g., ℝ², ℝ³, or other function spaces).

2. To determine if the given subset is a subspace, verify that it satisfies the following conditions:
  a. It contains the zero vector.
  b. It is closed under vector addition.
  c. It is closed under scalar multiplication.

If a given subset satisfies all of the above conditions, then it is a subspace of the identified vector space. If you can provide specific sets, I'd be happy to help you determine whether they are subspaces of a particular vector space.

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Answer:

I think it's D

Step-by-step explanation: Because 14 20 23 35 42 64 87 92 125 131 are the order so D can incase all of them

Answer:

32.16 degrees

Step-by-step explanation:

The angle of depression in these problems is always the same as the angle of elevation.

With that in mind, lets solve this problem.

So we are given 2 triangle lengths. The Hypotenuse is 898 ft, and the height of your triangle is 478 ft.

There are three trig functions, sine, cosine, and tangent, but we will be using sin for this triangle because he have the opposite side to the angle(see how the side labeled 478 ft is opposite to the angle of elevation?) and the hypotenuse.

Sin is defined as opposite/hypotenuse.

Now, we make our equation:

sin(478/898) = x

x is your answer, just plug it into a calculator.

You get 32.16 degrees

Answer:A."The theoretical probability, P(gold), is 25%

explanation:It's realy simple

Answer:x= 3/22

Step-by-step explanation:

Distribute

Subtract the numbers

Combine multiplied terms into a single fraction

Distribute

Find common denominator

Combine fractions with common denominator

Multiply the numbers

Add the numbers

The contrapositive of the given statement is “If their graph is a linear function, then the two variables are directly proportional”, option B is correct.

The contrapositive of a conditional statement switches the order of the clauses and negates them both. In general, the contrapositive of a conditional statement has the same truth value as the original statement.

It can be a useful tool in logic and proofs because it can help simplify the statement and make it easier to prove or disprove. For example, if we wanted to prove the original statement, we could instead prove its contrapositive, option B is correct.

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The complete question is:

What is the contrapositive of the conditional statement?

A) If their graph is not a linear function, then the two variables are not directly proportional.

B) If their graph is a linear function, then the two variables are directly proportional.

C) If two variables are not directly proportional, then their graph is not a linear function.

D) If their graph is a non-linear function, then the two variables are not directly proportional.

Answer: here

Step-by-step explanation:

Math is used in various careers such as construction. You will need to know the dimensions to make sure whatever it is being constructed is stable.

Math can help you financially. It can help you budget and prevent you from going into debt.

Math can help you understand real world problems better even if you may not use everything that you learn.

Answer:

Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art. It gives us a way to understand patterns, to quantify relationships, and to predict the future. Math helps us understand the world — and we use the world to understand math. The world is interconnected. Everyday math shows these connections and possibilities.

Step-by-step explanation:

1.we use mathematics for our daily living

2.from day care of school we started our mathematics lesson

3.mathematics is the most important specially when your in business 1.our daily living needs  simple mathematics to calculate. example; I buy a goods amounted 100 pesos then I have 500 pesos in my pocket so i am sure   400 pesos is my change.

2.From the very beginning or the early stage of our education we have to     start learning mathematics so the as we grow older math is in our brain system.

3.In business we know that math is very important because we calculate the capital, expenses, equals the profit.

4 multiplied by 25 using the distributive property is equal to 100.

The distributive property is a fundamental property in mathematics that states that multiplying a number by a sum is the same as multiplying the number by each addend in the sum and then adding the products.

In this case, we have 4 multiplied by the sum of 20 and 5, which can be rewritten as 4 multiplied by 20 plus 4 multiplied by 5. Thus:

4 × (20+5) = 4 × 20 + 4 × 5

= 80 + 20

= 100

Therefore, 4 multiplied by 25 using the distributive property is equal to 100.

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The final value of the annuity after 20 years of quarterly payments at a 5% interest rate compounded quarterly is:

$29,238.49.

To calculate the final value of the annuity, we can use the formula:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:
FV = Final value of the annuity
P = Quarterly payment ($200)
r = Annual interest rate (5%)
n = Number of compounding periods per year (4)
t = Number of years (20)

Plugging in the values, we get:

FV = 200 * ((1 + 0.05/4)^(4*20) - 1) / (0.05/4)
FV = $29,238.49

Therefore, the final value of the annuity after 20 years of quarterly payments at a 5% interest rate compounded quarterly is equal to $29,238.49.

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D'Angelo is reviewing potential sources for his research writing assignment and is considering an article with a different point of view. In this situation, he is using the Relevance aspect of the CRAAP method to determine if the article is appropriate for his paper.

The CRAAP method stands for Currency, Relevance, Authority, Accuracy, and Purpose, and helps evaluate the credibility and reliability of sources.

In this scenario, D'Angelo is reviewing an article that covers his topic, but from a different point of view that he is not considering in his thesis. While the article may be interesting, it may not be directly relevant to his research paper if it does not contribute to his thesis statement. D'Angelo is using the relevance aspect of the CRAAP method to evaluate whether or not to include this article in his research writing assignment. By doing so, he is ensuring that he uses sources that are directly relevant to his thesis and will help support his arguments.

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A web server is software and hardware that uses HTTP (Hypertext Transfer Protocol) and other protocols to respond to client requests made over the World Wide Web. The main job of a web server is to display website content by storing, processing, and delivering web pages to users.

To successfully switch the values of the variables x and y using a temporary variable called "temp," you can follow these steps:

1. Assign the value of x to the temporary variable: temp = x;
2. Assign the value of y to the variable x: x = y;
3. Assign the value stored in the temporary variable (temp) to the variable y: y = temp; By following these steps, the values of the variables x and y will be switched using the temporary variable "temp."The purpose of the break statement is to break out of a loop early. For example, if the following code asks you to input an integer number, x, If x is divisible by 5, the break statement is executed, and this causes the exit from the loop.The break statement ends the loop immediately when it is encountered. Its syntax is broken. The break statement is almost always used with an if-else statement inside the loop.

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Answer:

To find the slope of the tangent to the curve y = 4e^(3x) + (1/5)x + 4 at x = 1.5, we need to take the derivative of y with respect to x and evaluate it at x = 1.5.

The derivative of y with respect to x is:

dy/dx = 12e^(3x) + (1/5)

So, the slope of the tangent to the curve at x = 1.5 is:

dy/dx | x=1.5 = 12e^(3(1.5)) + (1/5)

dy/dx | x=1.5 = 12e^(4.5) + 0.2

dy/dx | x=1.5 ≈ 197.515

Therefore, the slope of the tangent to the curve y = 4e^(3x) + (1/5)x + 4 at x = 1.5 is approximately 197.515.

The slope of the tangent to the curve y = 4e^(3x) + 1/(5x) + 4 at x = 1.5 is approximately 512.558.

To find the slope of the tangent to the curve y = 4e^(3x) + 1/(5x) + 4 at x = 1.5, we need to take the derivative of y with respect to x and evaluate it at x = 1.5.

Taking the derivative of y with respect to x using the sum and power rules of differentiation, we get:

y' = 12e^(3x) - 1/(5x^2)

Now we substitute x = 1.5 to get:

y'(1.5) = 12e^(3(1.5)) - 1/(5(1.5)^2)

Simplifying, we get:

y'(1.5) = 12e^(4.5) - 1/11.25

Using a calculator, we can evaluate this expression to get:

y'(1.5) ≈ 512.558

Therefore, the slope of the tangent to the curve y = 4e^(3x) + 1/(5x) + 4 at x = 1.5 is approximately 512.558.

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a)

P(X = 2) = 0.1839

b)

P(X = 7) = 0.0573

c)

P(X = 1) = 0.3033

d)

P(X = 3) = 0.1413

We have,

a. To find P(X = 2) when λ = 2.5, we can use the Poisson probability mass function:

P(X = 2) = (e^(-λ)  x λ^X) / X!

Substituting λ = 2.5 and X = 2, we get:

P(X = 2) = (e^(-2.5) x 2.5²) / 2!

P(X = 2) ≈ 0.1839 (rounded to four decimal places)

b.

To find P(X = 7) when λ = 8.0, we can again use the Poisson probability mass function:

P(X = 7) = (e^(-λ) x λ^X) / X!

Substituting λ = 8.0 and X = 7, we get:

P(X = 7) = (e^(-8.0) x 8.0^7) / 7!

P(X = 7) ≈ 0.0573 (rounded to four decimal places)

c.

To find P(X = 1) when λ = 0.5, we use the same formula:

P(X = 1) = (e^(-λ) x λ^X) / X!

Substituting λ = 0.5 and X = 1, we get:

P(X = 1) = (e^(-0.5) * 0.5^1) / 1!

P(X = 1) ≈ 0.3033 (rounded to four decimal places)

d.

To find P(X = 3) when λ = 3.7, we can use the Poisson probability mass function:

P(X = 3) = (e^(-λ) * λ^X) / X!

Substituting λ = 3.7 and X = 3, we get:

P(X = 3) = (e^(-3.7) x 3.7³) / 3!

P(X = 3) ≈ 0.1413 (rounded to four decimal places)

Thus,

P(X = 2) = 0.1839

P(X = 7) = 0.0573

P(X = 1) = 0.3033

P(X = 3) = 0.1413

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There are 640 acres in 1 square mile. The area of a forest is increasing at a rate of 1 acre per decade. The rate at which the area of the forest is increasing, in square kilometers per decade is C) 0.0025 square kilometers per decade.

The area of the forest is increasing at a rate of 1 acre per decade. To find the rate in square kilometers per decade, we first need to convert acres to square miles, and then square miles to square kilometers.

1 acre = 1/640 square miles (since there are 640 acres in 1 square mile)

Now, we'll convert square miles to square kilometers using the given conversion factor (1 kilometer = 0.62 mile):

1/640 square miles * (1 km / 0.62 mile)^2 = 1/640 * (1 / 0.3844) square kilometers ≈ 0.00256 square kilometers

So, the closest answer to the rate at which the area of the forest is increasing is:

C) 0.0025 square kilometers per decade

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The length of the inventory cycle in days for the store when using an order quantity of 1,146 units per order is approximately 34.2216 days. To answer your question about the length of the inventory cycle in days for the store using an EOQ model and an order quantity of 1,146 units per order, we'll follow these steps:

Step:1. Calculate the EOQ (Economic Order Quantity) using the given information:
EOQ = √(2DS / H), where D is the annual demand, S is the ordering cost per order, and H is the holding cost per unit per year.
D = 10,054 units per year
S = $69 per order
H = 18% of the unit purchase cost ($83.4) = 0.18 * $83.4 = $15.012 per unit per year
EOQ = √(2 * 10,054 * 69 / 15.012) ≈ 1,146 units (the provided order quantity)
Step:2. Calculate the number of orders per year:
Number of Orders = Annual Demand / Order Quantity = 10,054 / 1,146 ≈ 8.7699 orders per year
Step:3. Calculate the inventory cycle length in days:
Inventory Cycle Length (Days) = (Operating Days per Year) / (Number of Orders per Year) = 300 / 8.7699 ≈ 34.2216 days
Therefore, the length of the inventory cycle in days for the store when using an order quantity of 1,146 units per order is approximately 34.2216 days.

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The matrix A will have one real eigenvalue of algebraic multiplicity 2 when k = -7.

To find the value of k for which matrix A has one real eigenvalue of algebraic multiplicity 2, we'll need to find the characteristic polynomial and solve for k. Here are the steps:

1. Write down matrix A:
A = | 2  k |
   |-3 -8 |

2. Find the characteristic polynomial by subtracting λ from the diagonal elements and finding the determinant of the resulting matrix:
| 2-λ  k  |
|-3   -8-λ |

3. Compute the determinant:
(2-λ)((-8)-λ) - (-3)(k) = λ^2 + 6λ + k + 16

4. The matrix A will have one real eigenvalue of algebraic multiplicity 2 if the characteristic polynomial has a double root. This occurs when the discriminant of the quadratic equation is equal to 0:
Δ = b^2 - 4ac = (6)^2 - 4(1)(k+16) = 0

5. Solve for k:
36 - 4(k+16) = 0
36 - 4k - 64 = 0
-4k = 28
k = -7

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The probability that they are all of different colors when a bag contains 9 marbles is 9/28.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Total number of marbles=9

Number of red marbles=3

Number of blue marbles=3

Number of yellow marbles=3

Three marbles are  selected from the bag at random probability that they are all different color:

[tex]\frac{^3C_1*^3C_1*^3C_1}{^9C_3} = \frac{9}{28}[/tex].

Therefore, the probability that they are all of different colors is 9/28.

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Complete question:

A bag contains 9 marbles, 3 of which are red, 3 of which are blue, and 3 of which are yellow. If three marbles are selected from the bag at random, what is probability that they are all of different colors?

The conclusion is that in a bowl containing 9 marbles, at least 3 of them are red, at least 3 are blue, or at least 5 are said to be green.

The use of Pigeonhole Principle to prove the statement will be done in this question.

The Pigeonhole Principle is one that states that if there are more pigeons than pigeonholes, then at least one pigeonhole needs to have  more than one pigeon.

So lets assume for contradiction that there are not at least 3 red marbles, 3 blue marbles, or 5 green marbles.

Case 1: There are fewer than 3 red marbles.

If less than 3 red marbles, then max 2 red marbles. 9 - 2 = 7 marbles left. 7 marbles: blue/green. With more than 3 marbles and assumed 2 red marbles, it violate the Pigeonhole Principle.

Case 2: There are fewer than 3 blue marbles.

If 3 blue marbles, then max 2 blue marbles. 9-2=7 marbles left, red or green. "More marbles than pigeonholes - against the Pigeonhole Principle."

Case 3: There are fewer than 5 green marbles.

5 green marbles, 4 green marbles. We have more marbles than pigeonholes,  so against the Pigeonhole Principle.

So, there is  contradiction in all 3 cases, our initial assumption that there are not at least 3 red marbles, 3 blue marbles, or 5 green marbles have to be  false.

So, we can say that in a bowl containing 9 marbles, at least 3 of them are red, at least 3 are blue, or at least 5 are green.

Another is:

Total number of marbles=9

Number of red marbles=3

Number of blue marbles=3

Number of yellow marbles=3

So, the probability that they are all of different colors is 9/28.

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The event that have a sample space of h and t would be Flipping a fair, two-sided coin. That is option A.

To calculate the possibility of selecting an outcome form an event the formula that should be used is given as follows;

Probability = possible outcome/sample space.

For a coin, the possible sample space = H and T when flipped only once.

Therefore, the event that have a sample space of h and t would be Flipping a fair, two-sided coin.

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The make of one keyboard guarantee should be for about 58 months, or approximately 5 years.

We can use the normal distribution to model the lifetime of the keyboards. Let X be the random variable representing the lifetime of the keyboards, and let μ = 6 and σ = 1.3 be the mean and standard deviation, respectively.

To find the length of guarantee such that no more than 5% of the keyboards need to be replaced under guarantee, we need to find the value x such that P(X < x) = 0.05. We can standardize the variable by subtracting the mean and dividing by the standard deviation:

Z = (X - μ) / σ

Using the standard normal distribution table or a calculator with a normal distribution function, we find that the z-score corresponding to a cumulative probability of 0.05 is approximately -1.645.

Therefore,

-1.645 = (x - 6) / 1.3

Solving for x, we get:

x = -1.645 * 1.3 + 6 = 4.83

So the length of guarantee should be approximately 4.83 years. Converting this to months, we get:

4.83 years * 12 months/year ≈ 58 months

Therefore, the guarantee should be for about 58 months, or approximately 5 years.

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The measure of the side x is 31. 509

First, we need to know the different trigonometric identities. These identities are;

From the information given, we have that;

The opposite side = x

The adjacent side = 45

The angle, theta = 35 degrees

Using the tangent identity, we have the ratio

tan 35 = x/45

cross multiply the values, we have;

x = 45tan (35)

find the value

x = 45(0. 7002)

multiply the values

x = 31. 509

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Answer:

They ate a total of 7.5 apples.

Step-by-step explanation:

The total number of apples that these 4 students ate is:

2 + 2.5 + 1.25 + 1.75 = 7.5

Therefore, they ate a total of 7.5 apples.

Answer: 7.5

Step-by-step explanation: 2 + 2.5 = 4.5

4.5 + 1.25 = 5.75

5.75 + 1.75 = 7.5

The quotient of 13,756 divided 5 is 2, 753.

We have to divide 13756 by 5.

So, the division is

                          5 | 13765 | 2 7 5 3

                                10

                              ____

                                   37

                                   35

                                 ____

                                      26

                                      25

                                     ___

                                         15

                                          15

                                         ___

                                           0

Thus, the quotient is 2,753.

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The term you are looking for is the proportion of the total variation in the dependent variable explained by the regression model (or independent variable), which is known as the A) coefficient of determination.

The coefficient of determination, also known as R-squared, is a statistical measure that indicates the proportion of the total variation in the dependent variable that is explained by the regression model or independent variable. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. The other terms mentioned - variable, proportion, and independent - are all related to the concept of regression analysis, which is used to identify the relationship between a dependent variable and one or more independent variables, and to quantify the extent to which changes in the independent variables affect the dependent variable.

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Answer:

a

Step-by-step explanation:

If $12,864 is invested in Jesaki Bank's 10-year CD that earns 2.3% compounded continuously, it will be worth $15,449.83 at maturity in 10 years. This calculation can be done using the formula:

A = Pe^(rt)

Where A is the amount at maturity, P is the principal amount (or initial investment), e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time period.

Substituting the given values, we get:

A = 12864 * e^(0.023*10)

A = 12864 * e^0.23

A = 12864 * 1.258871

A = 15,449.83

Therefore, the amount invested in Jesaki Bank's 10-year CD will be worth $15,449.83 at maturity in 10 years, rounded to the nearest cent.
To find the maturity value of the CD after 10 years, we will use the formula for continuous compounding:

A = P * e^(rt)

Where:
A = Maturity value
P = Principal amount invested (in this case, $12,864)
e = Base of the natural logarithm (approximately 2.71828)
r = Annual interest rate (in decimal form, 0.023 for 2.3%)
t = Time in years (10 years)

Step 1: Convert the annual interest rate to a decimal.
2.3% = 0.023

Step 2: Plug the given values into the continuous compounding formula.
A = $12,864 * e^(0.023 * 10)

Step 3: Calculate the exponent part of the formula.
0.023 * 10 = 0.23

Step 4: Calculate the maturity value.
A = $12,864 * e^0.23 ≈ $16,079.95

So, after 10 years, the maturity value of the $12,864 invested in the Jesaki Bank 10-year CD with 2.3% interest compounded continuously will be approximately $16,079.95, rounded to the nearest cent.

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The solution to the absolute value equation |x-3| > 4 is (-∞, -1) U (7, ∞) in interval notation

To solve the absolute value equation |x-3| > 4 and express the answer in interval notation, follow these steps:

1. Break the absolute value inequality into two separate inequalities:
  a) x - 3 > 4 (when x - 3 is positive)
  b) -(x - 3) > 4 (when x - 3 is negative)

2. Solve each inequality:
  a) x - 3 > 4 => x > 7
  b) -(x - 3) > 4 => -x + 3 > 4 => -x > 1 => x < -1

3. Write the solution in interval notation:
  (-∞, -1) U (7, ∞)

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