Integers

Absolute Value

The absolute value |x| is the distance from x to zero on the number line. It is always non-negative. Absolute value applies independently before other operations.

absolute-value The absolute value of x, written |x|: - |x| = x if x >= 0 - |x| = -x if x < 0 For an expression |a - b|: compute a - b first, then take the absolute value of the result.

Example

Evaluate absolute value as distance from zero.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

∣−7∣| -7 |
Locate -7; absolute value asks for distance to 0.0-7Distance is measured from the point to zero.

Step 2 — Distance from zero

Absolute value is distance from zero: |-7| = 7.

∣−7∣=7| -7 |= \hl{7}
-7 and 7 are the same distance from 0.0-77same distance: 7The distance from -7 to 0 is 7.

Step 3 — Expression

Set up the expression.

∣3−8∣| 3 - 8 |
First find the value inside |3 - 8|.03left 8Subtracting 8 from 3 moves left by 8.

Step 4 — Compute inside

Compute inside first: 3 - 8 = -5.

3−8=-53 - 8 = \hl{-5}
3 - 8 lands at -5.03left 8-5The inside value is -5.

Step 5 — Take absolute value

Now take the distance from zero: |-5| = 5.

∣−5∣=5| -5 |= \hl{5}
-5 and 5 are the same distance from 0.0-55same distance: 5The distance from -5 to 0 is 5.

Step 6 — Result

Read the final result.

757 \quad 5
Both answers are distances from 0.0-77distance 70-55distance 5Opposite points share a distance; absolute value reports that distance.