Solving Inequalities Practice
Solve like an equation. When you multiply or divide by a negative number, flip the inequality sign.
Last updated
Solve for x.
12 problems
- 1.
- 2.
- 3.
- 4.
- 5.
- 6.
- 7.6(x + 1) <= 18Answerx<=2
Move 6 to the other side
x+1<=3Move 1 to the other side
x<=2
- 8.1 <= 2x + 9 < 17Answer−4<=x; x<4
Subtract 9 from all parts
−8<=2×x; 2×x<8Divide all parts by 2
−4<=x; x<4
- 9.−1 <= 8 − x < 6Answer9>=x; x>2
Subtract 8 from all parts
−9<=−x; −x<−2Divide all parts by −1
9>=x; x>2
- 10.
- 11.6 − 7x <= x − 2Answer1<=x
Move −7×x to the other side
6<=8×x−2Move −2 to the other side
8<=8×xMove 8 to the other side
1<=x
- 12.3(x + 1) − 5x < x + 12Answerx>−3
Expand
3×x+3−5×x<x+12Move x to the other side
−3×x+3<12Move 3 to the other side
−3×x<9Move −3 to the other side
x>−3
For -3x ≤ 33, divide by -3 and flip: x ≥ -11. A compound inequality like 3 < x + 9 < 16 is solved on all three parts at once.
Common questions
- Why does the sign flip?
- Multiplying by a negative number reverses the order: 2 < 3, but -2 > -3.
- How do I write the answer?
- As an inequality like x > 4, or in interval notation as (4, ∞).
