Math worksheet for solving multi-step equations involving the distributive property and negative coefficients.

Absolutely! Let’s solve each of these multi-step equations that involve the distributive property and negative coefficients. The goal is to isolate the variable `x` on one side of the equation.

---

General Strategy:

1. Use the distributive property to eliminate parentheses.
2. Combine like terms.
3. Use inverse operations to isolate the variable.
4. Solve for `x`.

---

## ✔ Equation (1):
4x - 2(5x + 2) = 26

Step 1: Distribute the -2
→ 4x - 10x - 4 = 26

Step 2: Combine like terms
→ -6x - 4 = 26

Step 3: Add 4 to both sides
→ -6x = 30

Step 4: Divide by -6
→ x = -5

✔ Answer: x = -5

---

## ✔ Equation (2):
-36 = -5x + 4(2x - 3)

Step 1: Distribute the 4
→ -36 = -5x + 8x - 12

Step 2: Combine like terms
→ -36 = 3x - 12

Step 3: Add 12 to both sides
→ -24 = 3x

Step 4: Divide by 3
→ x = -8

✔ Answer: x = -8

---

## ✔ Equation (3):
-6x + 4(x + 2) = -4

Step 1: Distribute the 4
→ -6x + 4x + 8 = -4

Step 2: Combine like terms
→ -2x + 8 = -4

Step 3: Subtract 8 from both sides
→ -2x = -12

Step 4: Divide by -2
→ x = 6

✔ Answer: x = 6

---

## ✔ Equation (4):
-20 = -7x + 4(2x - 2)

Step 1: Distribute the 4
→ -20 = -7x + 8x - 8

Step 2: Combine like terms
→ -20 = x - 8

Step 3: Add 8 to both sides
→ -12 = x

✔ Answer: x = -12

---

## ✔ Equation (5):
42 = -3x + 7(x + 2)

Step 1: Distribute the 7
→ 42 = -3x + 7x + 14

Step 2: Combine like terms
→ 42 = 4x + 14

Step 3: Subtract 14 from both sides
→ 28 = 4x

Step 4: Divide by 4
→ x = 7

✔ Answer: x = 7

---

## ✔ Equation (6):
2x + 4(2x - 2) = 42

Step 1: Distribute the 4
→ 2x + 8x - 8 = 42

Step 2: Combine like terms
→ 10x - 8 = 42

Step 3: Add 8 to both sides
→ 10x = 50

Step 4: Divide by 10
→ x = 5

✔ Answer: x = 5

---

## ✔ Equation (7):
26 = 2x - 2(4x + 2)

Step 1: Distribute the -2
→ 26 = 2x - 8x - 4

Step 2: Combine like terms
→ 26 = -6x - 4

Step 3: Add 4 to both sides
→ 30 = -6x

Step 4: Divide by -6
→ x = -5

✔ Answer: x = -5

---

## ✔ Equation (8):
28 = 2x + 3(2x - 4)

Step 1: Distribute the 3
→ 28 = 2x + 6x - 12

Step 2: Combine like terms
→ 28 = 8x - 12

Step 3: Add 12 to both sides
→ 40 = 8x

Step 4: Divide by 8
→ x = 5

✔ Answer: x = 5

---

## ✔ Equation (9):
-15 = 3x + 6(-x + 2)

Step 1: Distribute the 6
→ -15 = 3x - 6x + 12

Step 2: Combine like terms
→ -15 = -3x + 12

Step 3: Subtract 12 from both sides
→ -27 = -3x

Step 4: Divide by -3
→ x = 9

✔ Answer: x = 9

---

## ✔ Equation (10):
-2x + 2(-x - 2) = -24

Step 1: Distribute the 2
→ -2x - 2x - 4 = -24

Step 2: Combine like terms
→ -4x - 4 = -24

Step 3: Add 4 to both sides
→ -4x = -20

Step 4: Divide by -4
→ x = 5

✔ Answer: x = 5

---

## 📋 Final Answers:

| Problem | Answer |
|---------|--------|
| (1) | x = -5 |
| (2) | x = -8 |
| (3) | x = 6 |
| (4) | x = -12 |
| (5) | x = 7 |
| (6) | x = 5 |
| (7) | x = -5 |
| (8) | x = 5 |
| (9) | x = 9 |
| (10) | x = 5 |

---

Let me know if you’d like to see any step explained in more detail! 😊