Practice Absolute Value in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The distance of a number from zero on the number line, always non-negative; written ∣x∣|x|. For any real number, absolute value strips away the sign and returns only the magnitude.

−5-5 and 55 are both 5 units from zero, so ∣−5∣=∣5∣=5|-5| = |5| = 5.

Showing a random 20 of 50 problems.

Example 1

medium
Compute (−9)2\sqrt{(-9)^2}.

Example 2

challenge
Solve ∣2x−1∣=∣x+4∣|2x - 1| = |x + 4|.

Example 3

easy
Compute ∣10−4∣|10-4|.

Example 4

easy
Compute ∣2−9∣|2-9|.

Example 5

medium
Evaluate ∣x∣|x| if x=−34x=-\frac{3}{4}.

Example 6

medium
Evaluate ∣3−8∣+∣−2∣−∣5∣|3 - 8| + |{-2}| - |5|.

Example 7

medium
Compute ∣2∣3−∣−3∣2|2|^3-|-3|^2.

Example 8

easy
Compute ∣3−8∣|3 - 8|.

Example 9

medium
If x>0x>0, simplify ∣x∣−x|x|-x.

Example 10

medium
Compute ∣−4∣⋅∣−3∣+∣2∣|-4|\cdot|-3|+|2|.

Example 11

medium
If x<0x<0, simplify ∣x∣+x|x|+x.

Example 12

challenge
For what real xx does ∣x−2∣=∣2−x∣|x-2|=|2-x| fail?

Example 13

easy
Fill in: ∣−3.5∣=|-3.5|= ____.

Example 14

easy
Compute ∣7∣|7|.

Example 15

easy
Compute ∣−8∣|-8|.

Example 16

hard
Compute ∣3−π∣+∣π−4∣|3-\pi|+|\pi-4|.

Example 17

easy
Compute ∣−2∣+∣5∣|-2| + |5|.

Example 18

medium
Solve ∣x−3∣=7|x - 3| = 7.

Example 19

easy
Compute ∣9∣|9|.

Example 20

easy
Compute −∣6∣-|6|.
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