50 Solving Two Step Inequalities Worksheet - Free Printable

Explanation:
We need to solve each inequality and match it with the correct interval (solution set). Let’s go one by one.

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1) $\frac{8x}{3} - 2x > 12$

First, combine like terms. Write $2x = \frac{6x}{3}$:

$$
\frac{8x}{3} - \frac{6x}{3} = \frac{2x}{3}
$$

So inequality becomes:
$$
\frac{2x}{3} > 12
$$

Multiply both sides by 3:
$$
2x > 36
$$

Divide by 2:
$$
x > 18
$$

Solution: $(18, \infty)$ → option b

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2) $\frac{7x + 1}{2} \ge 4$

Multiply both sides by 2:
$$
7x + 1 \ge 8
$$

Subtract 1:
$$
7x \ge 7
$$

Divide by 7:
$$
x \ge 1
$$

Solution: $[1, \infty)$ → option c

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3) $4(2 + 5x) < 48$

Distribute:
$$
8 + 20x < 48
$$

Subtract 8:
$$
20x < 40
$$

Divide by 20:
$$
x < 2
$$

Solution: $(-\infty, 2)$ → option a

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4) $3x + \frac{5x}{4} \le 34$

Get common denominator (4):
$$
\frac{12x}{4} + \frac{5x}{4} = \frac{17x}{4}
$$

So:
$$
\frac{17x}{4} \le 34
$$

Multiply both sides by 4:
$$
17x \le 136
$$

Divide by 17:
$$
x \le 8
$$

Solution: $(-\infty, 8]$ → option c

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5) $\frac{3x + 5}{2} \ge 7$

Multiply both sides by 2:
$$
3x + 5 \ge 14
$$

Subtract 5:
$$
3x \ge 9
$$

Divide by 3:
$$
x \ge 3
$$

Solution: $[3, \infty)$ → option d

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6) $9(3x - 13) \le 45$

Divide both sides by 9 first (easier):
$$
3x - 13 \le 5
$$

Add 13:
$$
3x \le 18
$$

Divide by 3:
$$
x \le 6
$$

Solution: $(-\infty, 6]$ → option c

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7) $\frac{3x}{2} + 5x \le 26$

Write $5x = \frac{10x}{2}$:

$$
\frac{3x}{2} + \frac{10x}{2} = \frac{13x}{2}
$$

So:
$$
\frac{13x}{2} \le 26
$$

Multiply both sides by 2:
$$
13x \le 52
$$

Divide by 13:
$$
x \le 4
$$

Solution: $(-\infty, 4]$ → option c

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8) $\frac{4x - 8}{6} > 2$

Multiply both sides by 6:
$$
4x - 8 > 12
$$

Add 8:
$$
4x > 20
$$

Divide by 4:
$$
x > 5
$$

Solution: $(5, \infty)$ → option b

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Let’s double-check each answer against options:

1) b
2) c
3) a
4) c
5) d
6) c
7) c
8) b

All steps verified.

Final Answer:
1) b
2) c
3) a
4) c
5) d
6) c
7) c
8) b