Allday Education

Free Solving Inequalities Worksheet

Ten two-step inequalities, including ones where dividing by a negative flips the symbol — with a complete answer key.

Answer key included
Name: Date:
Solving Inequalities
1.
9<11+10x9 < -11 + 10x
2.
2x3<92x - 3 < 9
3.
27>9+4x27 > -9 + 4x
4.
33>2+7x33 > -2 + 7x
5.
2x11<152x - 11 < -15
6.
1>2x7-1 > -2x - 7
7.
7x5377x - 5 \leq 37
8.
105x1510 \leq -5x - 15
9.
12+8x36-12 + 8x \geq 36
10.
11+3x1411 + 3x \geq 14
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Solving Inequalities
1.
9<11+10x9 < -11 + 10x
Answer: x>2x > 2
2.
2x3<92x - 3 < 9
Answer: x<6x < 6
3.
27>9+4x27 > -9 + 4x
Answer: x<9x < 9
4.
33>2+7x33 > -2 + 7x
Answer: x<5x < 5
5.
2x11<152x - 11 < -15
Answer: x<2x < -2
6.
1>2x7-1 > -2x - 7
Answer: x>3x > -3
7.
7x5377x - 5 \leq 37
Answer: x6x \leq 6
8.
105x1510 \leq -5x - 15
Answer: x5x \leq -5
9.
12+8x36-12 + 8x \geq 36
Answer: x6x \geq 6
10.
11+3x1411 + 3x \geq 14
Answer: x1x \geq 1
Andy · alldayeverydaymath.com

Scroll to see all 10 problems and the answer key on its own page. Printing includes every page.

About this worksheet

Inequalities work exactly like equations until a negative coefficient shows up, and that flip is what this sheet drills. Answers are written in solved form so students can check both the number and the direction of the symbol.

Students shaky on the skill itself? Send them to the free lesson: Solving Inequalities — explained step by step.

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