Solving Equations worksheet with eight algebra problems to find the value of the variable.

Let's solve each equation step by step.

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1) $ 2n - 15 = -5n + 4n $

Step 1: Simplify the right-hand side:
$$
-5n + 4n = -n
$$
So the equation becomes:
$$
2n - 15 = -n
$$

Step 2: Add $ n $ to both sides:
$$
2n + n - 15 = 0 \Rightarrow 3n - 15 = 0
$$

Step 3: Add 15 to both sides:
$$
3n = 15
$$

Step 4: Divide by 3:
$$
n = 5
$$

✔ Answer: $ n = 5 $

---

2) $ 5m - 4 = 2m + 8 $

Step 1: Subtract $ 2m $ from both sides:
$$
5m - 2m - 4 = 8 \Rightarrow 3m - 4 = 8
$$

Step 2: Add 4 to both sides:
$$
3m = 12
$$

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

✔ Answer: $ m = 4 $

---

3) $ 3p + 1 - 5 = -16 + 6p $

Step 1: Simplify both sides:
Left: $ 3p - 4 $
Right: $ -16 + 6p $

So:
$$
3p - 4 = -16 + 6p
$$

Step 2: Subtract $ 6p $ from both sides:
$$
3p - 6p - 4 = -16 \Rightarrow -3p - 4 = -16
$$

Step 3: Add 4 to both sides:
$$
-3p = -12
$$

Step 4: Divide by -3:
$$
p = 4
$$

✔ Answer: $ p = 4 $

---

4) $ -5k + 13 = 1 - 7k $

Step 1: Add $ 7k $ to both sides:
$$
-5k + 7k + 13 = 1 \Rightarrow 2k + 13 = 1
$$

Step 2: Subtract 13 from both sides:
$$
2k = 1 - 13 = -12
$$

Step 3: Divide by 2:
$$
k = -6
$$

✔ Answer: $ k = -6 $

---

5) $ 35 + 7n = 15 + 12n $

Step 1: Subtract $ 12n $ from both sides:
$$
35 + 7n - 12n = 15 \Rightarrow 35 - 5n = 15
$$

Step 2: Subtract 35 from both sides:
$$
-5n = 15 - 35 = -20
$$

Step 3: Divide by -5:
$$
n = 4
$$

✔ Answer: $ n = 4 $

---

6) $ 40 - 48v = -7 - v $

Step 1: Add $ v $ to both sides:
$$
40 - 48v + v = -7 \Rightarrow 40 - 47v = -7
$$

Step 2: Subtract 40 from both sides:
$$
-47v = -7 - 40 = -47
$$

Step 3: Divide by -47:
$$
v = 1
$$

✔ Answer: $ v = 1 $

---

7) $ 8r - 48 = -r - 3 $

Step 1: Add $ r $ to both sides:
$$
8r + r - 48 = -3 \Rightarrow 9r - 48 = -3
$$

Step 2: Add 48 to both sides:
$$
9r = -3 + 48 = 45
$$

Step 3: Divide by 9:
$$
r = 5
$$

✔ Answer: $ r = 5 $

---

8) $ 7 + 28n = 42 + 21n $

Step 1: Subtract $ 21n $ from both sides:
$$
7 + 28n - 21n = 42 \Rightarrow 7 + 7n = 42
$$

Step 2: Subtract 7 from both sides:
$$
7n = 35
$$

Step 3: Divide by 7:
$$
n = 5
$$

✔ Answer: $ n = 5 $

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✔ Final Answers:

1) $ n = 5 $
2) $ m = 4 $
3) $ p = 4 $
4) $ k = -6 $
5) $ n = 4 $
6) $ v = 1 $
7) $ r = 5 $
8) $ n = 5 $

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