FREE Solving and Graphing Inequalities Worksheets with Answer Key ... - Free Printable

Let’s solve each inequality one by one. We’ll find the solution for x, then describe how to graph it on the number line (since we can’t draw here, I’ll tell you exactly what to do).

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1) 3 ≤ x/4

Multiply both sides by 4:
3 × 4 ≤ x → x ≥ 12

Graph: Put a closed circle at 12 (because of “≥”), and shade to the right.

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2) 17 + x ≥ 13

Subtract 17 from both sides:
x ≥ 13 - 17 → x ≥ -4

Graph: Closed circle at -4, shade to the right.

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3) 16 ≥ x - 10

Add 10 to both sides:
16 + 10 ≥ x → x ≤ 26

Graph: Closed circle at 26, shade to the left.

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4) 25 > 5x

Divide both sides by 5:
25 ÷ 5 > x → x < 5

Graph: Open circle at 5 (because of “>”, not “≥”), shade to the left.

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5) 1 > x + 6

Subtract 6 from both sides:
1 - 6 > x → x < -5

Graph: Open circle at -5, shade to the left.

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6) 2 < x/9

Multiply both sides by 9:
2 × 9 < x → x > 18

Graph: Open circle at 18, shade to the right.

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7) 7x ≥ 35

Divide both sides by 7:
x ≥ 35 ÷ 7 → x ≥ 5

Graph: Closed circle at 5, shade to the right.

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8) 8 ≤ x - 14

Add 14 to both sides:
8 + 14 ≤ x → x ≥ 22

Graph: Closed circle at 22, shade to the right.

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Final Answer:
1) x ≥ 12
2) x ≥ -4
3) x ≤ 26
4) x < 5
5) x < -5
6) x > 18
7) x ≥ 5
8) x ≥ 22