Algebra 1 : How to find absolute value

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : How To Find Absolute Value

What number or numbers have absolute value  ?

Possible Answers:

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.

Example Question #1 : How To Find Absolute Value

What number or numbers have absolute value  ?

Possible Answers:

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.

Example Question #3 : How To Find Absolute Value

What number or numbers have absolute value 29?

Possible Answers:

No such number exists.

Correct answer:

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.

Example Question #4 : How To Find Absolute Value

What number or numbers have absolute value 11?

Possible Answers:

No such numbers exist.

Correct answer:

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.

Example Question #2 : How To Find Absolute Value

Evaluate the expression.

Possible Answers:

Correct answer:

Explanation:

First, simplify the terms in parentheses and absolute value.

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

Multiply and simplify.

Example Question #6 : How To Find Absolute Value

Solve for .

Possible Answers:

A solution does not exist.

Correct answer:

Explanation:

Divide both sides by .

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

  

or

Example Question #3 : 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.

Correct answer:

Explanation:

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

  which equals  

Example Question #8 : How To Find Absolute Value

Simplify the following equation:

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.

Then simplify the function

Example Question #9 : How To Find Absolute Value

Solve:  

Possible Answers:

Correct answer:

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 .

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.

Divide by negative one on both sides.

Subtract three on both sides.

Simplify both sides.

The answers to this question are:  

Example Question #10 : How To Find Absolute Value

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the following expression:

We can begin by changing the absolute value sign to a positive 16. 

We can do this because negative numbers within an absolute value sign should always be thought of as positive numbers.

Next, simplify your fraction to get

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