How many solutionsCompare both sides
Name: Date:
How many solutions does each equation have? Show how you know.
114x + 55 = 14x + 57
27x − 4 = 7x + 1
39x + 21 = 21 + 9x
4−8x − 54 = −54 − 8x
57x − 31 = 6x − 24
620x + 54 = 11x + 23
Number of solutions worksheets
Some equations have one answer, some none at all, and some are true for every number. These free printable worksheets ask which, from equations that need no expanding first.
If they get stuck
Number of 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 a mistake. There is none: the x really does cancel, and what is left — 2 = 5 — is never true, so no number works. That is the answer, and it is the most useful thing on the page.
Why this sheet works
The method is smaller than solving: collect the x terms and see what survives. An x left over means one solution; the x gone with a false statement means none; the x gone with a true statement means infinitely many. This is the direct half of the topic, where the equation is ready to compare as written — the expanding half, where a bracket has to be multiplied out first, is a separate page so this reading gets learned on its own.
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.
Number of solutions, step by step