How many solutionsMultiply out first
Name: Date:
Multiply out first, then say how many solutions. Show how you know.
14(2x − 3) = 8x − 12
22(−2x + 5) = 11x + 14
34(2x − 5) = −20x − 60
42(3x − 4) = 6x
55(2x − 1) = 10x − 5
62(4x − 6) = 8x − 4
Solutions after expanding worksheets
When a bracket sits in the way, the number of solutions cannot be read until it is multiplied out. These free printable worksheets ask how many solutions — after expanding first.
If they get stuck
Solutions after expanding
The answer key prints on a separate page.
What's on this sheet
2(x + 3) = 2x + 6 looks like it might have one solution until the bracket is opened: 2x + 6 = 2x + 6, the same on both sides, so every number works. 2(x + 3) = 2x + 5 expands to 2x + 6 = 2x + 5, which is never true, so none does. The expanding is the step that reveals the answer, and it is what this page is about.
Why this sheet works
None of these can be answered by reading the two sides as printed — that is the point of splitting them off from the direct page. A child has to distribute the bracket, then collect the x terms and see what is left, the same three outcomes as before: one solution, none, or infinitely many. It is the harder half of the same standard, and the one a test is most likely to use to tell real understanding from pattern-matching.
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.
Solutions after expanding, step by step