Algebra 1 Inequalities Worksheet with 10 problems to solve.

Let's solve each inequality step by step. We'll isolate the variable on one side of the inequality, just like solving equations, but remember: if you multiply or divide both sides by a negative number, you must reverse the inequality sign.

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1. $ 2x - 3 \leq 3 $

Add 3 to both sides:
$$
2x \leq 6
$$

Divide by 2:
$$
x \leq 3
$$

✔ Answer: $ x \leq 3 $

---

2. $ 2 - 3y > 16 $

Subtract 2 from both sides:
$$
-3y > 14
$$

Divide by -3 (remember to reverse the inequality):
$$
y < -\frac{14}{3}
$$

✔ Answer: $ y < -\frac{14}{3} $

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3. $ -10x + 2 < -18 $

Subtract 2 from both sides:
$$
-10x < -20
$$

Divide by -10 (reverse inequality):
$$
x > 2
$$

✔ Answer: $ x > 2 $

---

4. $ 3z - 6 \geq 21 $

Add 6 to both sides:
$$
3z \geq 27
$$

Divide by 3:
$$
z \geq 9
$$

✔ Answer: $ z \geq 9 $

---

5. $ 2v + 11 > 4v - 7 - 16 $

Simplify the right side:
$$
2v + 11 > 4v - 23
$$

Subtract $ 2v $ from both sides:
$$
11 > 2v - 23
$$

Add 23 to both sides:
$$
34 > 2v
$$

Divide by 2:
$$
17 > v \quad \text{or} \quad v < 17
$$

✔ Answer: $ v < 17 $

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6. $ 2.1x + 2.4 \geq 3.6x - 0.6 $

Subtract $ 2.1x $ from both sides:
$$
2.4 \geq 1.5x - 0.6
$$

Add 0.6 to both sides:
$$
3.0 \geq 1.5x
$$

Divide by 1.5:
$$
2 \geq x \quad \text{or} \quad x \leq 2
$$

✔ Answer: $ x \leq 2 $

---

7. $ 4x - 12 \geq 8 $

Add 12 to both sides:
$$
4x \geq 20
$$

Divide by 4:
$$
x \geq 5
$$

✔ Answer: $ x \geq 5 $

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8. $ 3x - 8 \leq 22 $

Add 8 to both sides:
$$
3x \leq 30
$$

Divide by 3:
$$
x \leq 10
$$

✔ Answer: $ x \leq 10 $

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9. $ 4(2y - 1) > -7 + 2y $

Distribute on the left:
$$
8y - 4 > -7 + 2y
$$

Subtract $ 2y $ from both sides:
$$
6y - 4 > -7
$$

Add 4 to both sides:
$$
6y > -3
$$

Divide by 6:
$$
y > -\frac{1}{2}
$$

✔ Answer: $ y > -\frac{1}{2} $

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10. $ 4(x - 1) \leq 16 $

Distribute:
$$
4x - 4 \leq 16
$$

Add 4 to both sides:
$$
4x \leq 20
$$

Divide by 4:
$$
x \leq 5
$$

✔ Answer: $ x \leq 5 $

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✔ Final Answers:

1. $ x \leq 3 $
2. $ y < -\frac{14}{3} $
3. $ x > 2 $
4. $ z \geq 9 $
5. $ v < 17 $
6. $ x \leq 2 $
7. $ x \geq 5 $
8. $ x \leq 10 $
9. $ y > -\frac{1}{2} $
10. $ x \leq 5 $

Let me know if you'd like these graphed on a number line!