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.
Ready to printAbsolute 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 this sheet, worked through a step at a time.
Solve |2x − 12| = 4
2x − 12 = 4or2x − 12 = −4
2x − 12 = 4→x = 8
2x − 12 = −4→x = 4
x = 4orx = 8
The bars mean the inside is 4 away from zero — so it is 4 OR it is −4. Split into two equations.
Solve the first, 2x − 12 = 4: add 12 to both sides: 2x = 16, then divide by 2: x = 8.
Solve the second, 2x − 12 = −4: add 12 to both sides: 2x = 8, then divide by 2: x = 4.
1. |2x − 12| = 4 → x = 4 or x = 82. |2x − 4| = 2 → x = 1 or x = 33. |2x + 4| = 4 → x = −4 or x = 04. |2x| = 8 → x = −4 or x = 45. |3x + 9| = 6 → x = −5 or x = −16. |2x| = 4 → x = −2 or x = 27. |2x − 6| = 10 → x = −2 or x = 88. |3x − 21| = 3 → x = 6 or x = 89. |3x − 3| = 12 → x = −3 or x = 510. |2x − 4| = 4 → x = 0 or x = 4
