How many solutionsBoth kinds
Name: Date:
How many solutions does each equation have? Show how you know.
117x − 37 = 17x − 33
26x − 18 = 15x + 40
35(2x − 3) = 10x − 15
44(2x + 6) = 8x + 24
513x − 26 = 13x − 22
616x + 30 = −13x + 57
How many solutions? worksheets
Some equations have one answer, some have none at all, and some are true for every number. These free printable worksheets ask which.
If they get stuck
How many solutions?
The answer key prints on a separate page.
What's on this sheet
A child who has only ever solved equations meets 3x + 2 = 3x + 5 as a dead end and assumes they made a mistake. They did not: the x really does disappear, and what is left — 2 = 5 — is never true, so no number works. That is the answer, not a failed calculation, and it is the single most useful thing on this page.
Why this sheet works
The method is the same for all three and it is a smaller question than solving: collect the x terms and see what survives. If an x is left, one value works. If the x vanishes and a false statement is left, nothing works. If the x vanishes and a true statement is left, everything does. A child who asks that question can answer an equation they have never seen.
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.
How many solutions?, step by step