# ACT Math : Absolute Value

## Example Questions

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### Example Question #1 : How To Find Absolute Value

Solve

All real numbers

No solutions

No solutions

Explanation:

Absolute values measure the distrance from the origin and is always positive, thus it can never be less than or equal to a negative number (unless a negative number is multiplied outside the absolute value).  So the correct answer is no solutions.

### Example Question #2 : How To Find Absolute Value

Explanation:

Absolute value is the key here. Absolute value means the number's distance from zero. So we must account for that. Therefore  .

### Example Question #2 : How To Find Absolute Value

What are the values of a and b, if any, where –a|b + 7| > 0?

a>0 and b not equal to 7

a<0 and b not equal to 7

a>0 and b not equal to 7

a<0 and b = 7

a<0 and b not equal to 7

Explanation:

The absolute value will always yield a positive, as long it is not zero. Therefore, b cannot equal 7. For the value to be positive, a must be a negative number.

### Example Question #4 : How To Find Absolute Value

What is the absolute value of 19 – 36(3) + 2(4 – 87)?

168

–255

–168

293

255

255

Explanation:

19 – 36(3) + 2(4 – 87) =

19 – 108 + 2(–83) =

19 – 108 – 166 = –255

Absolute value is the non-negative value of the expression

### Example Question #5 : How To Find Absolute Value

Solve for z where | z + 1 | < 3

z < 1 or z > 3x

1 < z

1 < z < 3

–4 < z < 2

–4 < z

–4 < z < 2

Explanation:

Absolute value problems generally have two answers:

z + 1 < 3 or z + 1 > –3 and subtracting 1 from each side gives z < 2 or z > –4 which bcomes –4 < z < 2

### Example Question #6 : How To Find Absolute Value

Find the absolute value of the following when x = 2,

Explanation:

and

It is important to know that the absolute value of something is always positive so the absolute value of  is

Evaluate for :

Explanation:

### Example Question #8 : How To Find Absolute Value

Evaluate for  :

Explanation:

Substitute 0.6 for  :

Evaluate for :

Explanation:

Substitute .

### Example Question #10 : How To Find Absolute Value

Which of the following sentences is represented by the equation

The absolute value of the sum of a number and seven is three less than the number.

The absolute value of the sum of a number and seven is three greater than the number.

None of the other responses are correct.

The sum of three and the absolute value of the sum of a number is three less than the number.

The sum of three and the absolute value of the sum of a number is three greater than the number.