Absolute value equationsSolve |ax + b| = c
Name: Date:
Solve each equation. Each has two answers.
1|2x − 12| = 4
2|2x − 4| = 2
3|2x + 4| = 4
4|2x| = 8
5|3x + 9| = 6
6|2x| = 4
7|2x − 6| = 10
8|3x − 21| = 3
9|3x − 3| = 12
10|2x − 4| = 4
Absolute value equations with coefficients worksheets
With a number in front of x, an absolute value equation adds one move to the split: after the bars become two equations, each still has a coefficient to divide away. These free printable worksheets practice |ax + b| = c, both answers per question.
If they get stuck
Absolute value equations with coefficients
The answer key prints on a separate page.
What's on this sheet
The split is the same as the entry level — the inside is c or −c — but the solving no longer stops there. |3x − 18| = 3 becomes 3x − 18 = 3 and 3x − 18 = −3; each is then a two-step equation, add 18 and divide by 3, giving x = 7 and x = 5. A child who forgets the divide, or who divides before splitting, loses the structure, so every step-by-step walk here splits first and solves each branch in full.
Why this sheet works
This is the reason it is a separate sheet from the basic one: the coefficient turns each of the two equations into a two-step solve, which is a real jump from a single add or subtract. Meeting it on its own, after the split is already secure, keeps the two-answer idea and the two-step solving from competing for attention.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Absolute value equations with coefficients, step by step