Linear Inequalities (one variable) worksheet with ten problems for solving inequalities.

Let’s solve each inequality step by step. We’ll isolate the variable $ x $ on one side, just like solving equations — but remember: if you multiply or divide by a negative number, flip the inequality sign! (None of these problems require that, so we’re safe.)

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1. $ 49 \geq 6x - 5 $

Add 5 to both sides:
$ 49 + 5 \geq 6x $ → $ 54 \geq 6x $

Divide both sides by 6:
$ 9 \geq x $ → or $ x \leq 9 $

✔ Final Answer for #1: $ x \leq 9 $

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2. $ 24 \geq 5x + 4 $

Subtract 4 from both sides:
$ 20 \geq 5x $

Divide by 5:
$ 4 \geq x $ → or $ x \leq 4 $

✔ Final Answer for #2: $ x \leq 4 $

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3. $ 7x + 7 \geq 63 $

Subtract 7 from both sides:
$ 7x \geq 56 $

Divide by 7:
$ x \geq 8 $

✔ Final Answer for #3: $ x \geq 8 $

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4. $ 31 > 7x + 3 $

Subtract 3 from both sides:
$ 28 > 7x $

Divide by 7:
$ 4 > x $ → or $ x < 4 $

✔ Final Answer for #4: $ x < 4 $

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5. $ 5x + 7 < 52 $

Subtract 7:
$ 5x < 45 $

Divide by 5:
$ x < 9 $

✔ Final Answer for #5: $ x < 9 $

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6. $ 8x + 3 > 19 $

Subtract 3:
$ 8x > 16 $

Divide by 8:
$ x > 2 $

✔ Final Answer for #6: $ x > 2 $

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7. $ 18 < 6x + 6 $

Subtract 6:
$ 12 < 6x $

Divide by 6:
$ 2 < x $ → or $ x > 2 $

✔ Final Answer for #7: $ x > 2 $

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8. $ 15 \leq 2x - 3 $

Add 3 to both sides:
$ 18 \leq 2x $

Divide by 2:
$ 9 \leq x $ → or $ x \geq 9 $

✔ Final Answer for #8: $ x \geq 9 $

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9. $ 3x + 8 < 29 $

Subtract 8:
$ 3x < 21 $

Divide by 3:
$ x < 7 $

✔ Final Answer for #9: $ x < 7 $

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10. $ 15 \leq 7x + 8 $

Subtract 8:
$ 7 \leq 7x $

Divide by 7:
$ 1 \leq x $ → or $ x \geq 1 $

✔ Final Answer for #10: $ x \geq 1 $

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Final Answer:
1. $ x \leq 9 $
2. $ x \leq 4 $
3. $ x \geq 8 $
4. $ x < 4 $
5. $ x < 9 $
6. $ x > 2 $
7. $ x > 2 $
8. $ x \geq 9 $
9. $ x < 7 $
10. $ x \geq 1 $