An absolute value equation has two answers because the bars mean distance: whatever is inside can be c above zero or c below it. These free printable worksheets stay at the entry level, |x + b| = c, so the splitting into two equations is the whole lesson.
The bars ask which numbers sit a fixed distance from a point. |x − 3| = 7 means the inside is 7 away from zero, so it is 7 or −7, splitting into x − 3 = 7 and x − 3 = −7 and giving 10 and −4. A child who writes only the first equation finds just the positive answer and misses half of every question, which is exactly the habit this level is built to fix — every step-by-step walk here writes both equations before solving either.
Why this sheet works
This is the version with no number in front of x, so once the bars are split each equation is a single add or subtract from its answer. Keeping the coefficient at one means the two-answer idea gets all the attention; the sheet with a coefficient in front, where a divide follows the split, is the next step and its own page.
How this one works
One question from this sheet, worked through a step at a time.
Solve |x| = 4
x = 4orx = −4
x = 4→x = 4
x = −4→x = −4
x = −4orx = 4
The bars mean the inside is 4 away from zero — so it is 4 OR it is −4. Split into two equations.
1. |x| = 4 → x = −4 or x = 42. |x + 2| = 5 → x = −7 or x = 33. |x − 1| = 4 → x = −3 or x = 54. |x − 3| = 6 → x = −3 or x = 95. |x − 1| = 3 → x = −2 or x = 46. |x − 2| = 9 → x = −7 or x = 117. |x + 3| = 2 → x = −5 or x = −18. |x − 6| = 6 → x = 0 or x = 129. |x + 4| = 4 → x = −8 or x = 010. |x − 5| = 6 → x = −1 or x = 11
