Multi-Step Equation Notes and Worksheets - Lindsay Bowden - Free Printable

Here is the complete solution for all 8 problems on the “Solving Multi-Step Equations Practice” worksheet, with step-by-step work shown.

---

1. Solve: `4(3x + 7) = 64 + 4x`

Step 1: Distribute the 4 on the left side.
```
12x + 28 = 64 + 4x
```

Step 2: Subtract 4x from both sides to get variables on one side.
```
12x - 4x + 28 = 64
8x + 28 = 64
```

Step 3: Subtract 28 from both sides.
```
8x = 64 - 28
8x = 36
```

Step 4: Divide by 8.
```
x = 36/8
x = 9/2 or x = 4.5
```

✔ Answer: `x = 9/2`

---

2. Solve: `16 = -4(2x - 5)`

Step 1: Distribute the -4 on the right side.
```
16 = -8x + 20
```

Step 2: Subtract 20 from both sides.
```
16 - 20 = -8x
-4 = -8x
```

Step 3: Divide both sides by -8.
```
x = (-4)/(-8)
x = 1/2
```

✔ Answer: `x = 1/2`

---

3. Solve: `-8(6 + 5x) = 3x - 5`

Step 1: Distribute the -8 on the left.
```
-48 - 40x = 3x - 5
```

Step 2: Add 40x to both sides to move variables to the right.
```
-48 = 43x - 5
```

Step 3: Add 5 to both sides.
```
-43 = 43x
```

Step 4: Divide by 43.
```
x = -43/43
x = -1
```

✔ Answer: `x = -1`

---

4. Solve: `33 = -3(1 + 4x)`

Step 1: Distribute the -3 on the right.
```
33 = -3 - 12x
```

Step 2: Add 3 to both sides.
```
36 = -12x
```

Step 3: Divide by -12.
```
x = 36 / (-12)
x = -3
```

✔ Answer: `x = -3`

---

5. Solve: `(4x - 2)/5 = 0.4`

Step 1: Multiply both sides by 5 to eliminate denominator.
```
4x - 2 = 0.4 × 5
4x - 2 = 2
```

Step 2: Add 2 to both sides.
```
4x = 4
```

Step 3: Divide by 4.
```
x = 1
```

✔ Answer: `x = 1`

---

6. Solve: `(2/3)x - 6 = (1/3)x + 3`

Step 1: Subtract `(1/3)x` from both sides.
```
(2/3)x - (1/3)x - 6 = 3
(1/3)x - 6 = 3
```

Step 2: Add 6 to both sides.
```
(1/3)x = 9
```

Step 3: Multiply both sides by 3.
```
x = 27
```

✔ Answer: `x = 27`

---

7. Find the mistake and correct it: `(1/4)(12x - 16) = 2x`

This problem likely expects you to solve the equation and show where a common mistake might occur.

Let’s solve it correctly first:

Correct Solution:
Distribute `1/4`:
```
(1/4)(12x) - (1/4)(16) = 2x
3x - 4 = 2x
```

Subtract 2x from both sides:
```
x - 4 = 0
x = 4
```

✔ Correct Answer: `x = 4`

Common Mistake:
A student might forget to distribute the `1/4` to both terms inside the parentheses and only multiply `1/4 × 12x`, ignoring `-16`. That would give:
```
3x = 2x → x = 0 (wrong!)
```

Correction:
Always distribute to every term inside the parentheses. The correct solution is `x = 4`.

---

8. Find the mistake and correct it: `-4 + 14x = -12 + 12x`

Let’s solve correctly:

Correct Solution:
Subtract 12x from both sides:
```
-4 + 2x = -12
```

Add 4 to both sides:
```
2x = -8
```

Divide by 2:
```
x = -4
```

✔ Correct Answer: `x = -4`

Common Mistake:
A student might incorrectly combine constants and variables — for example, adding 4 to both sides but forgetting to subtract 12x, leading to:
```
14x = -8 + 12x → then maybe 2x = -8 → x = -4 (accidentally correct?)
```
But if they mistakenly did:
```
-4 + 14x = -12 + 12x
→ 14x - 12x = -12 - 4 → 2x = -16 → x = -8 (WRONG)
```
They might have subtracted 4 instead of adding 4.

Actually, the most common mistake here is misaligning signs when moving terms.

Correction:
Move variable terms to one side and constants to the other carefully:
```
-4 + 14x = -12 + 12x
→ 14x - 12x = -12 + 4
→ 2x = -8
→ x = -4
```

✔ Final Answer: `x = -4`

---

## ✔ Final Answers Summary:

1. `x = 9/2`
2. `x = 1/2`
3. `x = -1`
4. `x = -3`
5. `x = 1`
6. `x = 27`
7. Mistake: Not distributing `1/4` to both terms. Correct: `x = 4`
8. Mistake: Sign error when moving terms. Correct: `x = -4`

Let me know if you’d like this formatted as a printable answer key!