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ACT Math : Integers

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Example Questions

Example Question #1 : How To Find Absolute Value

$\left | 7 - 2\right | - \left | 4 - 8\right | =?$

Possible Answers:

Correct answer:

Explanation:

Absolute value is the key here. Absolute value means the number's distance from zero. So we must account for that. Therefore $\left | 4-8\right |$ $= \left | -4\right | = 4$ .

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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 = –7

a>0 and b not equal to 7

a>0 and b not equal to –7

a<0 and b not equal to –7

Correct answer:

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.

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Example Question #3 : How To Find Absolute Value

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

Possible Answers:

–255

293

–168

168

255

Correct answer:

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

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Example Question #4 : Absolute Value

Solve for z where | z + 1 | < 3

Possible Answers:

1 < z < 3

–4 < z < 2

1 < z

–4 < z

z < 1 or z > 3x

Correct answer:

–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

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Example Question #171 : Integers

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

$\left | \frac{x^3-12}{2}\right |$

Possible Answers:

Correct answer:

Explanation:

$2^{3}=8$

8-12=-4 and $\frac{-4}{2}=-2$

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

2 is your answer.

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Example Question #171 : Integers

Evaluate for x = 2 :

$\left | 2x - 18 \right | + \left | 3x - 7 \right |$

Possible Answers:

Correct answer:

Explanation:

$\left | 2x -18 \right | + \left | 3x - 7 \right |$

$= \left | 2 \cdot 2 - 18 \right | + \left | 3 \cdot 2 - 7 \right |$

$= \left | 4 - 18 \right | + \left | 6 - 7 \right |$

$= \left | -14 \right | + \left | -1 \right |$

=14 + 1 = 15

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Example Question #171 : Integers

Evaluate for x = 0.6 :

$\left | 4x - 1.4 \right | + \left | x^{2} - 1 \right |$

Possible Answers:

0.64

1.64

1.36

0.36

2.36

Correct answer:

1.64

Explanation:

Substitute 0.6 for :

$\left | 4x - 1.4 \right | + \left | x^{2} - 1 \right |$

$= \left | 4 \cdot 0.6 - 1.4 \right | + \left | 0.6^{2} - 1 \right |$

$= \left | 2.4 - 1.4 \right | + \left | 0.36 - 1 \right |$

$= \left | 1 \right | + \left | -0.64 \right |$

=1 + 0.64

= 1.64

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Example Question #172 : Integers

Evaluate for x = 0.6 :

$\left |0.5 x - 0.7 \right | - \left |0.6 x - 0.4 \right |$

Possible Answers:

0.44

1.04

0.76

0.96

0.36

Correct answer:

0.36

Explanation:

Substitute x = 0.6 .

$\left |0.5 x - 0.7 \right | - \left |0.6 x - 0.4 \right |$

$= \left |0.5 \cdot 0.6 - 0.7 \right | - \left |0.6 \cdot 0.6 - 0.4 \right |$

$= \left |0.3- 0.7 \right | - \left |0.36 - 0.4 \right |$

$= \left |-0.4 \right | - \left | - 0.04 \right |$

= 0.4 - 0.04 = 0.36

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Example Question #881 : Arithmetic

Which of the following sentences is represented by the equation

| x + 7 | = x - 3

Possible Answers:

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

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 less than the number.

None of the other responses are correct.

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

Correct answer:

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

Explanation:

| x + 7 | is the absolute value of x+ 7 , 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 x - 3 , 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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Example Question #173 : Integers

Define $f(x) = |3x - |x^{2}- 7|\; |$

Evaluate f(2) .

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

$f(x) = |3x - |x^{2}- 7|\; |$

$f(2) = |3 \cdot 2 - |2^{2}- 7|\; |$

$= |3 \cdot 2 - |4- 7|\; |$

$= |3 \cdot 2 - |-3|\; |$

$= |3 \cdot 2 -3 |$

= |6 -3 |

= | 3 |

= 3

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ACT Math : Integers

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find Absolute Value

Example Question #2 : How To Find Absolute Value

Example Question #3 : How To Find Absolute Value

Example Question #4 : Absolute Value

Example Question #171 : Integers

Example Question #171 : Integers

Example Question #171 : Integers

Example Question #172 : Integers

Example Question #881 : Arithmetic

Example Question #173 : Integers

All ACT Math Resources

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