13+ Simple Algebra Worksheet Templates -Word, PDF - Free Printable

Let's solve each of these multi-step equations step by step. I'll go through them one at a time, showing the steps clearly and explaining the process.

---

1) $-20 = -4x - 6x$

Step 1: Combine like terms on the right side:
$$
-4x - 6x = -10x
$$
So:
$$
-20 = -10x
$$

Step 2: Divide both sides by $-10$:
$$
x = \frac{-20}{-10} = 2
$$

✔ Answer: $x = 2$

---

2) $6 = 1 - 2n + 5$

Step 1: Simplify the right side:
$$
1 + 5 = 6 \Rightarrow 6 = 6 - 2n
$$

Step 2: Subtract 6 from both sides:
$$
6 - 6 = -2n \Rightarrow 0 = -2n
$$

Step 3: Divide by $-2$:
$$
n = 0
$$

✔ Answer: $n = 0$

---

3) $8x - 2 = -9 + 7x$

Step 1: Move all $x$-terms to one side. Subtract $7x$ from both sides:
$$
8x - 7x - 2 = -9 \Rightarrow x - 2 = -9
$$

Step 2: Add 2 to both sides:
$$
x = -9 + 2 = -7
$$

✔ Answer: $x = -7$

---

4) $a + 5 = -5a + 5$

Step 1: Add $5a$ to both sides:
$$
a + 5a + 5 = 5 \Rightarrow 6a + 5 = 5
$$

Step 2: Subtract 5 from both sides:
$$
6a = 0
$$

Step 3: Divide by 6:
$$
a = 0
$$

✔ Answer: $a = 0$

---

5) $4m - 4 = 4m$

Step 1: Subtract $4m$ from both sides:
$$
4m - 4m - 4 = 0 \Rightarrow -4 = 0
$$

This is not true, so no solution exists.

✘ Answer: No solution (contradiction)

---

6) $p - 1 = 5p + 3p - 8$

Step 1: Combine like terms on the right:
$$
5p + 3p = 8p \Rightarrow p - 1 = 8p - 8
$$

Step 2: Subtract $p$ from both sides:
$$
-1 = 7p - 8
$$

Step 3: Add 8 to both sides:
$$
7 = 7p
$$

Step 4: Divide by 7:
$$
p = 1
$$

✔ Answer: $p = 1$

---

7) $5p - 14 = 8p + 4$

Step 1: Subtract $5p$ from both sides:
$$
-14 = 3p + 4
$$

Step 2: Subtract 4:
$$
-18 = 3p
$$

Step 3: Divide by 3:
$$
p = -6
$$

✔ Answer: $p = -6$

---

8) $p - 4 = -9 + p$

Step 1: Subtract $p$ from both sides:
$$
-4 = -9
$$

✘ This is false → No solution

✔ Answer: No solution

---

9) $-8 = -(x + 4)$

Step 1: Distribute the negative sign:
$$
-8 = -x - 4
$$

Step 2: Add 4 to both sides:
$$
-4 = -x
$$

Step 3: Multiply both sides by $-1$:
$$
x = 4
$$

✔ Answer: $x = 4$

---

10) $12 = -4(-6x - 3)$

Step 1: Distribute $-4$:
$$
-4 \cdot (-6x) = 24x,\quad -4 \cdot (-3) = 12
\Rightarrow 12 = 24x + 12
$$

Step 2: Subtract 12 from both sides:
$$
0 = 24x
$$

Step 3: Divide by 24:
$$
x = 0
$$

✔ Answer: $x = 0$

---

11) $14 = -(p - 8)$

Step 1: Distribute the negative:
$$
14 = -p + 8
$$

Step 2: Subtract 8:
$$
6 = -p
$$

Step 3: Multiply by $-1$:
$$
p = -6
$$

✔ Answer: $p = -6$

---

12) $-(7 - 4x) = 9$

Step 1: Distribute the negative:
$$
-7 + 4x = 9
$$

Step 2: Add 7 to both sides:
$$
4x = 16
$$

Step 3: Divide by 4:
$$
x = 4
$$

✔ Answer: $x = 4$

---

13) $-18 - 6k = 6(1 + 3k)$

Step 1: Distribute on the right:
$$
6 \cdot 1 = 6,\quad 6 \cdot 3k = 18k \Rightarrow -18 - 6k = 6 + 18k
$$

Step 2: Add $6k$ to both sides:
$$
-18 = 6 + 24k
$$

Step 3: Subtract 6:
$$
-24 = 24k
$$

Step 4: Divide by 24:
$$
k = -1
$$

✔ Answer: $k = -1$

---

14) $5n + 34 = -2(1 - 7n)$

Step 1: Distribute $-2$:
$$
-2 \cdot 1 = -2,\quad -2 \cdot (-7n) = 14n \Rightarrow 5n + 34 = -2 + 14n
$$

Step 2: Subtract $5n$:
$$
34 = -2 + 9n
$$

Step 3: Add 2:
$$
36 = 9n
$$

Step 4: Divide by 9:
$$
n = 4
$$

✔ Answer: $n = 4$

---

15) $2(4x - 3) - 8 = 4 + 2x$

Step 1: Distribute $2$:
$$
8x - 6 - 8 = 4 + 2x \Rightarrow 8x - 14 = 4 + 2x
$$

Step 2: Subtract $2x$:
$$
6x - 14 = 4
$$

Step 3: Add 14:
$$
6x = 18
$$

Step 4: Divide by 6:
$$
x = 3
$$

✔ Answer: $x = 3$

---

16) $3n - 5 = -8(6 + 5n)$

Step 1: Distribute $-8$:
$$
-8 \cdot 6 = -48,\quad -8 \cdot 5n = -40n \Rightarrow 3n - 5 = -48 - 40n
$$

Step 2: Add $40n$ to both sides:
$$
43n - 5 = -48
$$

Step 3: Add 5:
$$
43n = -43
$$

Step 4: Divide by 43:
$$
n = -1
$$

✔ Answer: $n = -1$

---

17) $-(1 + 7x) - 6(-7 - x) = 36$

Step 1: Distribute negatives:
$$
-1 - 7x + 42 + 6x = 36
$$

Step 2: Combine like terms:
$$
(-7x + 6x) + (-1 + 42) = -x + 41 = 36
$$

Step 3: Subtract 41:
$$
-x = -5
$$

Step 4: Multiply by $-1$:
$$
x = 5
$$

✔ Answer: $x = 5$

---

18) $-3(4x + 3) + 4(6x + 1) = 43$

Step 1: Distribute:
$$
-3 \cdot 4x = -12x,\quad -3 \cdot 3 = -9
\Rightarrow -12x - 9
$$
$$
4 \cdot 6x = 24x,\quad 4 \cdot 1 = 4 \Rightarrow 24x + 4
$$
Now combine:
$$
-12x - 9 + 24x + 4 = 43 \Rightarrow 12x - 5 = 43
$$

Step 2: Add 5:
$$
12x = 48
$$

Step 3: Divide by 12:
$$
x = 4
$$

✔ Answer: $x = 4$

---

## ✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $x = 2$ |
| 2) | $n = 0$ |
| 3) | $x = -7$ |
| 4) | $a = 0$ |
| 5) | No solution |
| 6) | $p = 1$ |
| 7) | $p = -6$ |
| 8) | No solution |
| 9) | $x = 4$ |
| 10) | $x = 0$ |
| 11) | $p = -6$ |
| 12) | $x = 4$ |
| 13) | $k = -1$ |
| 14) | $n = 4$ |
| 15) | $x = 3$ |
| 16) | $n = -1$ |
| 17) | $x = 5$ |
| 18) | $x = 4$ |

Let me know if you'd like these checked or explained further!