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.
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 this sheet, worked through a step at a time.
14x + 55 = 14x + 57
14x + 55 = 14x + 57
14x + 55 = 14x + 57
x is gone
55 = 57— never true
no solution
Do not start by hunting for x. Ask a smaller question first: what is left when the x terms are collected on one side?
Both sides have the SAME number of x, so taking it off both sides removes x completely. That is not a mistake — it is the answer arriving early.
What is left is 55 = 57, which is never true, whatever x is. So there is no solution.
