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Algebra 1 : Number Lines and Absolute Value

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Example Questions

Example Question #2 : Number Lines

Plot the fraction $-\frac{7}{3}$ on the number line.

Possible Answers:

Question_11_correct

Question_11_incorrect_3

Question_11_incorrect_1

Question_11_incorrect_2

Correct answer:

Question_11_correct

Explanation:

The fraction $-\frac{7}{3}$ is less than and greater than , so it must fall between those points on the number line. Negative numbers are to the left of while positive numbers are to the right.

$-\frac{7}{3}=-2\frac{1}{3}$

Because $\frac{1}{3}$ is less than $\frac{1}{2}$ , the point must be closer to than .

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Example Question #1 : Number Lines And Absolute Value

What number or numbers have absolute value ?

Possible Answers:

No such numbers exist.

-7,7

-7,-14,-21,-28...

Correct answer:

No such numbers exist.

Explanation:

The absolute value of every real number is nonnegative, so no number with absolute value can exist.

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Example Question #2 : How To Find Absolute Value

What number or numbers have absolute value ?

Possible Answers:

$\left \{ -13, -26, -39, -52,...\right \}$

-13, 13

No such numbers exist.

Correct answer:

No such numbers exist.

Explanation:

The absolute value of every real number is nonnegative, so no number with absolute value can exist.

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Example Question #2 : Number Lines And Absolute Value

What number or numbers have absolute value 29?

Possible Answers:

$\left \{ -29, -58,-87,-116,...\right \}$

-29, 29

No such number exists.

Correct answer:

-29, 29

Explanation:

The absolute value of any positive number is the number itself, so 29 has 29 as an absolute value. Also, the absolute value of a negative number is its (positive) opposite, so also has 29 as an absolute value.

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Example Question #4 : How To Find Absolute Value

What number or numbers have absolute value 11?

Possible Answers:

$\left \{ -11, -22,-33,-44,-55,...\right \}$

No such numbers exist.

-11,11

Correct answer:

-11,11

Explanation:

The absolute value of any positive number is the number itself, so 11 has 11 as an absolute value. Also, the absolute value of a negative number is its (positive) opposite, so also has 11 as an absolute value.

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Example Question #1 : Number Lines And Absolute Value

Evaluate the expression.

$\small 3(\frac{(8-10)^2}{\left | 8-10 \right |})$

Possible Answers:

Correct answer:

Explanation:

$\small 3(\frac{(8-10)^2}{\left | 8-10 \right |})$

First, simplify the terms in parentheses and absolute value.

$3(\frac{-2^2}{\left | -2 \right |})$

Remember that the absolute value of a negative term is positive.

$3(\frac{4}{2})$

Multiply and simplify.

$\frac{3*4}{2}=\frac{12}{2}=6$

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Example Question #2 : Number Lines And Absolute Value

Solve for .

$-3\left | p+2 \right |=-12$

Possible Answers:

p=2, -6

p=2,6

p=-2,-6

p=-2,6

A solution does not exist.

Correct answer:

p=2, -6

Explanation:

Divide both sides by .

$\frac{-3\left | p+2 \right |}{-3}=\frac{-12}{-3}$

$\left | p+2 \right |=4$

Remove the absolute value brackets by setting the expression equal to both the positive and negative values of 4:

p+2=4

p=2

p+2=-4

p=-6

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Example Question #5 : How To Find Absolute Value

Mr. Smith and his wife went on a trip, they travelled miles towards their destination, however on the way there they had to turn around and drive miles away from their destination to get Mr. Smith's wallet from the store. After getting his wallet they drove more miles to reach their destination. What is the total number of miles that the family covered?

Possible Answers:

Not enough information.

$25\:miles$

$40\:miles$

$45\:miles$

$50\:miles$

Correct answer:

$50\:miles$

Explanation:

Even though the Smiths travelled backwards you still have to add the positive number to the equation. So it looks like this:

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Example Question #9 : Number Lines And Absolute Value

Simplify the following equation:

$\left | -9\right |-\left | 4\right |$

Possible Answers:

Correct answer:

Explanation:

It is important to understand that the absolute value is the distance from a number is.

To simply this equation you need to simplify the absolute values first.

$\left | -9\right |=9$

$\left | 4\right |=4$

Then simplify the function

9-4=5

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Example Question #3 : Number Lines And Absolute Value

Solve: $\left | x+3\right | = 5$

Possible Answers:

-8, -2

-8, 2

Correct answer:

-8, 2

Explanation:

In order to solve this absolute value, we will need to split up the absolute value in its positive and negative solution.

Break up the absolute value and rewrite the terms for the positive solution and solve for .

x+3=5

x=2

For the negative solution, split up the absolute value and add a negative in front of the quantity which was contained by the absolute value.

-(x+3)=5

Divide by negative one on both sides.

x+3=-5

Subtract three on both sides.

x+3-3=-5-3

Simplify both sides.

x=-8

The answers to this question are: -8, 2

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Algebra 1 : Number Lines and Absolute Value

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2 : Number Lines

Example Question #1 : Number Lines And Absolute Value

Example Question #2 : How To Find Absolute Value

Example Question #2 : Number Lines And Absolute Value

Example Question #4 : How To Find Absolute Value

Example Question #1 : Number Lines And Absolute Value

Example Question #2 : Number Lines And Absolute Value

Example Question #5 : How To Find Absolute Value

Example Question #9 : Number Lines And Absolute Value

Example Question #3 : Number Lines And Absolute Value

All Algebra 1 Resources

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