The distance of x from zero on the number line.
Free Interactive Pre-Algebra Tool
Absolute Value Practice
Learn absolute value as distance from zero. Evaluate expressions, compare absolute values, identify missing numbers, and solve absolute value equations using a visual number line.
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Learn why absolute value represents distance from zero, how opposite numbers can have the same absolute value, and how to solve basic absolute value equations.
Read the Absolute Value Guide
Practice Mode
Find the distance of a number from zero.
Problem 1 of 10
10%
Current Problem
Use distance from zero to evaluate the absolute value.
Evaluate
Beginner
Problem
|−7|
Evaluate the absolute value.
1
Locate Number
2
Find Distance
3
Evaluate
Step 1
Locate the number on the number line
Find −7 relative to zero.
Current Problem
|−7|
Number Line Lab
Locate −7 on the number line.
Distance: 7
Current number
Opposite number
Equation solution
Absolute Value Meaning
Absolute value measures distance from zero.
|−7| = 7
−7 is 7 units from zero, so its absolute value is 7.
Compare Distances
Compare the absolute values, not just the original numbers.
|−7|
7
units from zero
>
|4|
4
units from zero
Distance Equation
Which numbers are 6 units from zero?
Left of zero
x = −6
and
Right of zero
x = 6
Your Work
How far is −7 from zero?
Choose the correct answer.
Start by locating the number relative to zero.
Hint
Distance is always nonnegative.
Absolute Value Reference
Opposite numbers are the same distance from zero.
Distance cannot be negative, so absolute value is always zero or positive.
If a > 0, there are usually two solutions: x = −a and x = a.
Think distance, not sign-changing.
|−8| = 8
|8| = 8
|0| = 0
|x| = 5 → x = −5 or 5
Important: the absolute value bars are grouping symbols. Simplify what is inside the bars first when the expression contains arithmetic.
Problem Complete
|−7| = 7
−7 is 7 units from zero, so its absolute value is 7.
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You completed all 10 absolute value problems.
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Distance From Zero
Absolute value tells you how many units a number is from zero on the number line.
Opposite Numbers
Numbers such as −6 and 6 have the same absolute value because they are equally far from zero.
Compare Distances
Comparing absolute values means comparing distances from zero rather than comparing the original signs.
Solve Equations
An equation such as |x| = 5 asks which numbers are exactly 5 units from zero.
Complete Example
Solve |x| = 6
Absolute value represents distance, so ask which numbers are exactly 6 units from zero.
|x| = 6
1
Interpret the equation
x must be 6 units from zero
2
Look left of zero
−6 is 6 units away
3
Look right of zero
6 is also 6 units away
Therefore, x = −6 or x = 6. The two solutions are opposite numbers because they lie the same distance from zero.
Practice Absolute Value Step by Step
Absolute value is a foundational pre-algebra concept that describes the distance between a number and zero. Because distance cannot be negative, absolute value is always zero or positive.
This interactive absolute value practice tool uses a visual number line to help students understand the meaning behind the notation instead of simply memorizing a rule about changing signs.
How to Evaluate Absolute Value
To evaluate an absolute value, determine the distance of the number inside the bars from zero. For example, −8 is 8 units from zero, so |−8| = 8. The number 8 is also 8 units from zero, so |8| = 8.
Absolute Value as Distance From Zero
Thinking of absolute value as distance explains why opposite numbers have the same absolute value and why absolute value results cannot be negative.
Comparing Absolute Values
When comparing absolute values, compare each number's distance from zero. For example, |−9| is greater than |4| because 9 is farther from zero than 4.
Solving Absolute Value Equations
An equation such as |x| = 7 asks for every number whose distance from zero is 7. There are two such numbers: −7 and 7. More advanced absolute value equations use the same distance idea after the expression inside the bars has been isolated.
Expressions Inside Absolute Value Bars
Absolute value bars also act as grouping symbols. When arithmetic appears inside the bars, simplify that expression first and then take its absolute value. For example, |−4 + 9| becomes |5|, which equals 5.
Three Difficulty Levels
Beginner practice focuses on integers and distance from zero. Intermediate problems add comparisons, missing values, and basic equations. Advanced practice can include multi-step expressions, larger values, and absolute value equations involving two solutions or special cases.