SAT Math : How to find absolute value

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Find Absolute Value

Define .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

, or, equivalently,

Example Question #11 : How To Find Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Find Absolute Value

Define .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #882 : Arithmetic

Solve 

Possible Answers:

No solution

Correct answer:

Explanation:

Since this is an absolute value equation, we must set the left hand side equal to both the positive and negative versions of the right side. Therefore,

Solving the first equation, we see that 

Solving the second, we see that 

When we substitute each value back into the original equation  , we see that they both check.

Example Question #11 : How To Find Absolute Value

Solve:

Possible Answers:

None of the given answers. 

Correct answer:

Explanation:

To solve this equation, we want to set  equal to both  and  and solve for .

Therefore:

and

We can check both of these answers by plugging them back into the inequality to see if the statement is true. 

and

Both answers check, so our final answer is 

Example Question #881 : Arithmetic

Solve:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we want to set what's inside the absolute value signs equal to the positive and negative value on the right side of the equation. That's because the value inside the absolute value symbols could be equivalent to  or , and the equation would still hold true.

So let's set  equal to  and  separately and solve for our unknown.

First:

Second:

Therefore, our answers are  and 

Example Question #12 : How To Find Absolute Value

Evaluate the expression if  and .

Possible Answers:

Correct answer:

Explanation:

To solve, we replace each variable with the given value.

Simplify. Remember that terms inside of the absolute value are always positive.

Example Question #891 : Arithmetic

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

Simplify the following:

Begin with basic subtraction:

Next, remember what we do with absolute value signs; we change negative values to positive values, and positive values remain positive.

So our answer is positive 51

Example Question #11 : How To Find Absolute Value

Solve for all possible values of x. 

Possible Answers:

Correct answer:

Explanation:

When solving for x in the presence of absolute value, there are always two answers.

To eliminate the absolute value, the equation must be re-written two ways:

 and 

 and 

 and 

 and 

 and 

 

Example Question #1 : Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate 

Possible Answers:

Both  and 

Correct answer:

Explanation:

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