### All ACT Math Resources

## Example Questions

### Example Question #167 : Integers

Solve

**Possible Answers:**

No solutions

All real numbers

**Correct answer:**

No solutions

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 #1 : Absolute Value

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

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

**Correct answer:**

a<0 and b not equal to **–**7

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 #2 : Absolute Value

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

**Possible Answers:**

293

168

–168

255

–255

**Correct answer:**

255

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 #3 : Absolute Value

Solve for z where | z + 1 | < 3

**Possible Answers:**

1 < z

–4 < z

–4 < z < 2

1 < z < 3

z < 1 or z > 3x

**Correct answer:**

–4 < z < 2

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 #171 : Integers

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

**Possible Answers:**

**Correct answer:**

and

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

2 is your answer.

### Example Question #1 : Absolute Value

Evaluate for :

**Possible Answers:**

**Correct answer:**

### Example Question #7 : How To Find Absolute Value

Evaluate for :

**Possible Answers:**

**Correct answer:**

Substitute 0.6 for :

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

Evaluate for :

**Possible Answers:**

**Correct answer:**

Substitute .

### Example Question #9 : How To Find Absolute Value

Which of the following sentences is represented by the equation

**Possible Answers:**

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

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

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

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

None of the other responses are correct.

**Correct answer:**

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

is the absolute value of , which in turn is the sum of a number and seven and a number. Therefore, can be written as "the absolute value of the sum of a number and seven". Since it is equal to , it is three less than the number, so the equation that corresponds to the sentence is

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

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