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Solving inequalities worksheets

An inequality is solved almost exactly like an equation, and the one place it differs is the place everybody loses marks. These free printable worksheets keep the steps to one and put the sign itself in the answer.

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Solving inequalities
Solving inequalities worksheet — One step, sign included, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

x + 7 > 12 comes apart the same way x + 7 = 12 does: take seven off both sides. The answer is x > 5, and the difference from an equation is that it names a whole range rather than one number — everything above five works, and five itself does not.

Why this sheet works

Then there is the rule. Multiplying or dividing both sides by a negative flips the sign, so −2x < 8 gives x > −4 rather than x < −4. It is worth checking rather than remembering: put −5 in and see whether it satisfies the original. A child who can test an answer never needs to recall which way the sign went.

How this one works

One question from this sheet, worked through a step at a time.

x − 10 > 15

x − 10 > 15
15+10=25
>
x>25
  1. An inequality comes apart exactly like an equation — the same moves, done to both sides. There is one extra rule and it arrives at the end, so start by ignoring the sign and solving for x.
  2. 10 was taken away last, so it goes back on first — onto BOTH sides: 15 + 10 = 25.
  3. Nothing was divided by a negative here, so the sign has not moved: it is still >. That is the one thing to check on every one of these before writing the answer down.
  4. So x > 25. That is a whole RANGE of numbers rather than one, which is what makes this different from an equation — and why the sign is half the answer.

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