Numbers & Operations
Absolute Value
Absolute value is the distance a number is from zero on the number line — it is always positive or zero.
Visualize It
Absolute Value = Distance from Zero on the Number Line
Example 1 — Find |−8|
-8 is 8 units away from zero, so |−8| = 8
Example 2 — Solve |x| = 5
Both −5 and 5 are exactly 5 units from zero → x = −5 or x = 5
Example 3 — Compare |−12| and |9|
|−12| = 12 units from zero, |9| = 9 units from zero → |−12| > |9|
Key Insight
Absolute value is always zero or positive — distance can never be negative.
|−8| = 8 · |8| = 8 · |0| = 0
Watch & Learn
Watch a clear, friendly video explanation of Absolute Value:
Watch on YouTube →Opens a YouTube search for the best tutorial videos on this topic.
Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Find |−8|
Step-by-Step Solution
Absolute value means distance from zero.
-8 is 8 units away from zero.
|−8| = 8
Answer
8
Problem
Solve: |x| = 5
Step-by-Step Solution
We need all numbers whose distance from zero is 5.
Both 5 and -5 are exactly 5 units from zero.
So x = 5 or x = -5.
Answer
x = 5 or x = -5
Problem
Compare: |−12| and |9|
Step-by-Step Solution
|−12| = 12 (distance of -12 from zero)
|9| = 9 (distance of 9 from zero)
12 > 9, so |−12| > |9|
Answer
|−12| > |9|
Problem
Evaluate: |3 − 10|
Step-by-Step Solution
First compute inside the absolute value: 3 − 10 = −7.
Then take the absolute value: |−7| = 7.
Answer
7
Problem
Is |−4| equal to |4|? Explain.
Step-by-Step Solution
|−4| = 4 (distance of −4 from zero is 4 units).
|4| = 4 (distance of 4 from zero is 4 units).
Yes — they are equal because absolute value measures distance, not direction.
Answer
Yes, |−4| = |4| = 4
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Find |−15|
Find |7|
Solve: |x| = 11
Which is greater: |−20| or |15|?
Find |0|
Evaluate: |−6 + 2|
Evaluate: |5 − 12|
Solve: |x| = 0
Is |−3| greater than, less than, or equal to |3|?
Evaluate: |−100|
Find |−2.5|
Which is farther from zero: −8 or 6?
Finished all 12? Give yourself a pat on the back — then check your work!
Keep going — you're on a roll!
Every topic you master is another step on your journey.
Explore More Topics