### All SAT Math Resources

## Example Questions

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

Define .

Evaluate .

**Possible Answers:**

**Correct answer:**

, or, equivalently,

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

Define an operation as follows:

For all real numbers ,

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #13 : How To Find Absolute Value

Define .

Evaluate .

**Possible Answers:**

**Correct answer:**

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

Solve

**Possible Answers:**

No solution

**Correct answer:**

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:

**Possible Answers:**

None of the given answers.

**Correct answer:**

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 #16 : How To Find Absolute Value

Solve:

**Possible Answers:**

**Correct answer:**

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 #881 : Arithmetic

Evaluate the expression if and .

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

Both and

**Correct answer:**

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