# SAT Math : How to find absolute value

## Example Questions

### Example Question #11 : How To Find Absolute Value

Define .

Evaluate .

Explanation:

, or, equivalently,

### Example Question #12 : How To Find Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate .

Explanation:

Define .

Evaluate .

Explanation:

### Example Question #14 : How To Find Absolute Value

Solve

No solution

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 #15 : How To Find Absolute Value

Solve:

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

### Example Question #16 : How To Find Absolute Value

Solve:

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:

### Example Question #881 : Arithmetic

Evaluate the expression if  and .

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 #18 : How To Find Absolute Value

Simplify the following:

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 #19 : How To Find Absolute Value

Solve for all possible values of x.

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 : How To Find Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate