Algebra
Solving inequalities
Same moves as equations — except multiplying by a negative flips the sign.
Solve inequalities the same way as equations — except multiplying or dividing by a negative flips the sign.
Walk through
Step 1 of 4
Start
Solve −2x + 1 ≤ 7. Treat ≤ like = for now.
Watch out
The classic slip: forgetting to flip the inequality sign when you multiply or divide both sides by a negative number. −3x < 9 becomes x > −3, not x < −3. Adding or subtracting a negative does not flip it — only multiplying/dividing by one does.
Your turn
Solve 5 − 3x > 11.
Recap
- Solve inequalities like equations — isolate the variable.
- Multiplying or dividing by a negative flips ≤↔≥ and <↔>.
- Sanity-check by testing a value from your solution set.
Try it
−2x > 6
Divide by −2 and flip: x < −3.
Multiplying by a negative is the only move that flips ≤ to ≥. Don't forget!