One-variable Inequalities Themed Math Worksheets | Age 10-12 - Free Printable

Let's solve each inequality step by step. I'll solve them one at a time, showing the process clearly.

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1) $ x - 3 > 10 $

Add 3 to both sides:

$$
x > 10 + 3 \\
x > 13
$$

✔ Answer: $ x > 13 $

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2) $ x + 5 > 12 $

Subtract 5 from both sides:

$$
x > 12 - 5 \\
x > 7
$$

✔ Answer: $ x > 7 $

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3) $ 2x - 7 > 20 $

Add 7 to both sides:

$$
2x > 20 + 7 \\
2x > 27
$$

Divide both sides by 2:

$$
x > \frac{27}{2} \\
x > 13.5
$$

✔ Answer: $ x > 13.5 $

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4) $ -4x + 11 > 13 $

Subtract 11 from both sides:

$$
-4x > 13 - 11 \\
-4x > 2
$$

Now divide by -4. Remember: When dividing by a negative number, reverse the inequality sign.

$$
x < \frac{2}{-4} \\
x < -0.5
$$

✔ Answer: $ x < -0.5 $

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5) $ 8x + 24 > 10 $

Subtract 24 from both sides:

$$
8x > 10 - 24 \\
8x > -14
$$

Divide by 8:

$$
x > \frac{-14}{8} \\
x > -\frac{7}{4} \quad \text{or} \quad x > -1.75
$$

✔ Answer: $ x > -1.75 $

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6) $ x + 4 < 12 $

Subtract 4 from both sides:

$$
x < 12 - 4 \\
x < 8
$$

✔ Answer: $ x < 8 $

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7) $ x - 22 < -11 $

Add 22 to both sides:

$$
x < -11 + 22 \\
x < 11
$$

✔ Answer: $ x < 11 $

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8) $ 3x - 14 < 12 $

Add 14 to both sides:

$$
3x < 12 + 14 \\
3x < 26
$$

Divide by 3:

$$
x < \frac{26}{3} \approx 8.67
$$

✔ Answer: $ x < \frac{26}{3} $ or $ x < 8.\overline{6} $

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9) $ -6x + 40 < 30 $

Subtract 40 from both sides:

$$
-6x < 30 - 40 \\
-6x < -10
$$

Divide by -6 (reverse inequality):

$$
x > \frac{-10}{-6} \\
x > \frac{5}{3} \approx 1.67
$$

✔ Answer: $ x > \frac{5}{3} $

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10) $ 9x - 35 < 50 $

Add 35 to both sides:

$$
9x < 50 + 35 \\
9x < 85
$$

Divide by 9:

$$
x < \frac{85}{9} \approx 9.44
$$

✔ Answer: $ x < \frac{85}{9} $

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✔ Final Answers:

| Problem | Solution |
|--------|----------|
| 1) $ x - 3 > 10 $ | $ x > 13 $ |
| 2) $ x + 5 > 12 $ | $ x > 7 $ |
| 3) $ 2x - 7 > 20 $ | $ x > 13.5 $ |
| 4) $ -4x + 11 > 13 $ | $ x < -0.5 $ |
| 5) $ 8x + 24 > 10 $ | $ x > -1.75 $ |
| 6) $ x + 4 < 12 $ | $ x < 8 $ |
| 7) $ x - 22 < -11 $ | $ x < 11 $ |
| 8) $ 3x - 14 < 12 $ | $ x < \frac{26}{3} $ |
| 9) $ -6x + 40 < 30 $ | $ x > \frac{5}{3} $ |
| 10) $ 9x - 35 < 50 $ | $ x < \frac{85}{9} $ |

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🕒 Time Tracking (Example):

Since this is a simulated response, here’s how you'd fill it in:

> Time Started: 10:00 AM
> Time Finished: 10:10 AM

(You can replace with your actual start and end times.)

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Let me know if you'd like these answers graphed on a number line or explained further!