Solving inequalities worksheets
Thirty-six inequality questions: reading number line graphs, writing inequalities from sentences, testing solutions, solving one-step and two-step inequalities with the flip rule, and solving then graphing.
Download the free inequalities worksheet (PDF)
Inequalities worksheet
What’s on the worksheet
- 36 questions on inequalities, sized for US Letter paper
- 2 pages of questions plus an answer key on the last page
- Written for grades 6–7, matching Common Core 6.EE.B.8, 7.EE.B.4b
- Name and date lines at the top, and room to show the work
Sample questions from this worksheet
- 0 x _____ Part B • Write an inequality for each sentence. Use x for the unknown
- You must be at least 12 years old.
- Fewer than 30 people fit in the room.
- The speed limit is 55 miles an hour.
- The temperature stayed above −5°C.
- A score of more than 80 wins a prize.
Preview the worksheet and answer key
Make a new inequalities worksheet
Need another page for extra practice, a retake or a second group in class? The free Mathify Kids test maker builds a fresh inequalities worksheet with different numbers every time. Choose how many questions, print it with its own answer key, or let your child take it on screen and see the score straight away.
Inequalities: a worked example (−3x + 2 ≥ 14)
- Subtract 2 from both sides: −3x ≥ 12.
- Divide both sides by −3. Dividing by a negative flips the sign: x ≤ −4.
- Graph it with a filled circle at −4 and an arrow to the left.
- Test a point: x = −5 gives 15 + 2 = 17, and 17 ≥ 14 is true.
How to use it at home and in class
At home
Part A and Part B are the grade 6 skills, so start there for younger children. For Parts D and E, ask “did I multiply or divide by a negative?” before writing the sign. Testing one number from the answer, as in Part C, catches almost every flip mistake in seconds. Ten problems a day works better than a whole sheet at once. Mark them together with the answer key, then ask your child to explain one they got wrong: finding the mistake themselves is where the learning happens.
In class
Use the first row as a warm-up, a full page for independent practice, or five questions as an exit ticket. For a retake or a second group, make a new version with the test maker so every child gets different numbers.
Mistakes to watch for
- Forgetting to flip the sign after multiplying or dividing by a negative number.
- Flipping the sign when adding or subtracting a negative, which never needs a flip.
- Using an open circle for ≤ or ≥. Those include the boundary, so the circle is filled.
- Reading “at least” as < instead of ≥.
What to practice before and after inequalities
- Before: evaluating expressions. If this sheet is a struggle, go back a step.
- After: equation word problems, once this one is mostly right.
- Learn it first: the inequalities lesson.
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Questions parents ask
When do you flip the inequality sign?
Only when you multiply or divide both sides by a negative number. Adding or subtracting, even a negative number, never flips the sign.
What grade is this inequalities worksheet for?
It is written for grades 6–7 and matches Common Core standards 6.EE.B.8, 7.EE.B.4b.
Can I get a different version of this inequalities worksheet?
Yes. Use the free Mathify Kids test maker to make a new inequalities worksheet with different numbers every time. You choose how many questions, and every version comes with its own answer key.