Practice worksheet for solving two-step inequalities, featuring eight problems aligned with Common Core Standard 7.EE.4.

Let's solve each of the two-step inequalities step by step. The goal is to isolate the variable $ x $ on one side of the inequality.

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1) $ 9x - 9 > 9 $

Step 1: Add 9 to both sides
$$
9x - 9 + 9 > 9 + 9 \\
9x > 18
$$

Step 2: Divide both sides by 9
$$
x > \frac{18}{9} \\
x > 2
$$

✔ Answer: $ x > 2 $

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2) $ 3x + 25 < 35 $

Step 1: Subtract 25 from both sides
$$
3x + 25 - 25 < 35 - 25 \\
3x < 10
$$

Step 2: Divide both sides by 3
$$
x < \frac{10}{3}
$$

✔ Answer: $ x < \frac{10}{3} $ or $ x < 3.\overline{3} $

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3) $ -10x + 14 \geq 134 $

Step 1: Subtract 14 from both sides
$$
-10x + 14 - 14 \geq 134 - 14 \\
-10x \geq 120
$$

Step 2: Divide both sides by -10
⚠️ Remember: When dividing by a negative number, reverse the inequality sign.
$$
x \leq \frac{120}{-10} \\
x \leq -12
$$

✔ Answer: $ x \leq -12 $

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4) $ 20 + 7x > 97 $

Step 1: Subtract 20 from both sides
$$
20 + 7x - 20 > 97 - 20 \\
7x > 77
$$

Step 2: Divide both sides by 7
$$
x > \frac{77}{7} \\
x > 11
$$

✔ Answer: $ x > 11 $

---

5) $ -x + 4 \geq 15 $

Step 1: Subtract 4 from both sides
$$
-x + 4 - 4 \geq 15 - 4 \\
-x \geq 11
$$

Step 2: Multiply both sides by -1 (and reverse the inequality)
$$
x \leq -11
$$

✔ Answer: $ x \leq -11 $

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6) $ 0.25x + 3 \leq -7 $

Step 1: Subtract 3 from both sides
$$
0.25x + 3 - 3 \leq -7 - 3 \\
0.25x \leq -10
$$

Step 2: Divide both sides by 0.25
$$
x \leq \frac{-10}{0.25} \\
x \leq -40
$$

✔ Answer: $ x \leq -40 $

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7) $ -x - 8 < 31 $

Step 1: Add 8 to both sides
$$
-x - 8 + 8 < 31 + 8 \\
-x < 39
$$

Step 2: Multiply both sides by -1 (reverse inequality)
$$
x > -39
$$

✔ Answer: $ x > -39 $

---

8) $ -4x - 6 > 10 $

Step 1: Add 6 to both sides
$$
-4x - 6 + 6 > 10 + 6 \\
-4x > 16
$$

Step 2: Divide both sides by -4 (reverse inequality)
$$
x < \frac{16}{-4} \\
x < -4
$$

✔ Answer: $ x < -4 $

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✔ Final Answers:

1) $ x > 2 $
2) $ x < \frac{10}{3} $
3) $ x \leq -12 $
4) $ x > 11 $
5) $ x \leq -11 $
6) $ x \leq -40 $
7) $ x > -39 $
8) $ x < -4 $

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🔍 Key Tips:

- Always perform the same operation on both sides.
- If you multiply or divide by a negative number, flip the inequality sign.
- Simplify fractions when possible.

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