This worksheet provides eight practice problems for solving multi-step linear equations with one variable.

Let’s solve each equation step by step. We’ll combine like terms, isolate the variable, and simplify carefully.

---

1. Solve for x: 9 = 3 – x – 2x

Combine the x terms on the right:
–x – 2x = –3x
So:
9 = 3 – 3x

Subtract 3 from both sides:
9 – 3 = –3x → 6 = –3x

Divide both sides by –3:
x = 6 ÷ (–3) = –2

✔ Check: Plug x = –2 into original:
3 – (–2) – 2(–2) = 3 + 2 + 4 = 9 ✔️

---

2. Solve for c: –c – 4c – 5 = 0

Combine c terms:
–c – 4c = –5c
So:
–5c – 5 = 0

Add 5 to both sides:
–5c = 5

Divide by –5:
c = 5 ÷ (–5) = –1

✔ Check: –(–1) – 4(–1) – 5 = 1 + 4 – 5 = 0 ✔️

---

3. Solve for b: –36 = 12 – 2b – 4b

Combine b terms:
–2b – 4b = –6b
So:
–36 = 12 – 6b

Subtract 12 from both sides:
–36 – 12 = –6b → –48 = –6b

Divide by –6:
b = (–48) ÷ (–6) = 8

✔ Check: 12 – 2(8) – 4(8) = 12 – 16 – 32 = –36 ✔️

---

4. Solve for x: –9 + 3x + 2x = –49

Combine x terms:
3x + 2x = 5x
So:
–9 + 5x = –49

Add 9 to both sides:
5x = –40

Divide by 5:
x = –40 ÷ 5 = –8

✔ Check: –9 + 3(–8) + 2(–8) = –9 –24 –16 = –49 ✔️

---

5. Solve for k: 11 + 3k – 2k = 17

Combine k terms:
3k – 2k = k
So:
11 + k = 17

Subtract 11:
k = 17 – 11 = 6

✔ Check: 11 + 3(6) – 2(6) = 11 + 18 – 12 = 17 ✔️

---

6. Solve for c: –4(2c – 7) – 2c = 38

First, distribute the –4:
–4 × 2c = –8c
–4 × (–7) = +28
So:
–8c + 28 – 2c = 38

Combine c terms:
–8c – 2c = –10c
So:
–10c + 28 = 38

Subtract 28:
–10c = 10

Divide by –10:
c = 10 ÷ (–10) = –1

✔ Check: –4(2(–1) – 7) – 2(–1) = –4(–2 –7) + 2 = –4(–9) + 2 = 36 + 2 = 38 ✔️

---

7. Solve for k: 160 = 4(–4k + 10) – 4k

Distribute the 4:
4 × (–4k) = –16k
4 × 10 = 40
So:
160 = –16k + 40 – 4k

Combine k terms:
–16k – 4k = –20k
So:
160 = –20k + 40

Subtract 40:
120 = –20k

Divide by –20:
k = 120 ÷ (–20) = –6

✔ Check: 4(–4(–6) + 10) – 4(–6) = 4(24 + 10) + 24 = 4(34) + 24 = 136 + 24 = 160 ✔️

---

8. Solve for x: 4(–4x – 5) – 3x = –172

Distribute the 4:
4 × (–4x) = –16x
4 × (–5) = –20
So:
–16x – 20 – 3x = –172

Combine x terms:
–16x – 3x = –19x
So:
–19x – 20 = –172

Add 20 to both sides:
–19x = –152

Divide by –19:
x = (–152) ÷ (–19) = 8

✔ Check: 4(–4(8) – 5) – 3(8) = 4(–32 –5) – 24 = 4(–37) – 24 = –148 – 24 = –172 ✔️

---

Final Answer:
1. x = –2
2. c = –1
3. b = 8
4. x = –8
5. k = 6
6. c = –1
7. k = –6
8. x = 8