InequalitiesTo 50
Name: Date:
Solve each one, then write >, <, ≥ or ≤ in the box.
1−4x > 44x−11
2−9x ≥ −45x5
32x < −6x−3
42x < 4x2
5−8x > −48x6
69x > 18x2
7−9x > −27x3
89x < 9x1
Multiplication and division inequalities worksheets
Multiplying or dividing an inequality by a negative flips the sign — the one rule that separates inequalities from equations, and where most marks are lost. These free printable worksheets drill exactly that.
If they get stuck
Multiplication and division inequalities
The answer key prints on a separate page.
What's on this sheet
3x < 12 is solved like an equation: divide both sides by 3 to get x < 4, sign unchanged. But −2x < 8 divides by a negative, so the sign turns over — x > −4, not x < −4. Both kinds sit on every sheet, because a page of only positives never triggers the flip and teaches a rule that is silently wrong the first time a negative coefficient appears.
Why this sheet works
The answer includes the sign, so a solution with the right number and the wrong direction is marked as wrong — which is the only way the flip is actually learned. It is worth testing rather than memorizing: put a number from the range back into the original and see whether it holds. This is the multiplication-and-division cut of solving inequalities, kept apart from the addition-and-subtraction one so the flip gets its own page.
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.
Multiplication and division inequalities, step by step