Solving Algebraic Equations worksheet - Free Printable

Let's solve each equation step by step, following the principles shown in the examples provided.

---

Section A – Solving One Step Equations

We solve these by performing the inverse operation to isolate the variable.

#### (a) $ w + 4 = 10 $

To isolate $ w $, subtract 4 from both sides:

$$
w = 10 - 4 = 6
$$

✔ Answer: $ w = 6 $

---

#### (b) $ y - 2 = 9 $

Add 2 to both sides:

$$
y = 9 + 2 = 11
$$

✔ Answer: $ y = 11 $

---

#### (c) $ 6m = 42 $

Divide both sides by 6:

$$
m = \frac{42}{6} = 7
$$

✔ Answer: $ m = 7 $

---

#### (d) $ a - 25 = 5 $

Add 25 to both sides:

$$
a = 5 + 25 = 30
$$

✔ Answer: $ a = 30 $

---

#### (e) $ \frac{b}{5} = 40 $

Multiply both sides by 5:

$$
b = 40 \times 5 = 200
$$

✔ Answer: $ b = 200 $

---

#### (f) $ 5 + k = 12 $

Subtract 5 from both sides:

$$
k = 12 - 5 = 7
$$

✔ Answer: $ k = 7 $

---

Section B – Solving Two Step Equations

These require two operations: first undo addition/subtraction, then multiplication/division.

#### (a) $ 6a + 2 = 20 $

Step 1: Subtract 2 from both sides:

$$
6a = 20 - 2 = 18
$$

Step 2: Divide both sides by 6:

$$
a = \frac{18}{6} = 3
$$

✔ Answer: $ a = 3 $

---

#### (b) $ 2d + 4 = 10 $

Step 1: Subtract 4:

$$
2d = 10 - 4 = 6
$$

Step 2: Divide by 2:

$$
d = \frac{6}{2} = 3
$$

✔ Answer: $ d = 3 $

---

#### (c) $ 4z - 8 = 8 $

Step 1: Add 8 to both sides:

$$
4z = 8 + 8 = 16
$$

Step 2: Divide by 4:

$$
z = \frac{16}{4} = 4
$$

✔ Answer: $ z = 4 $

---

#### (d) $ 3c - 6 = 15 $

Step 1: Add 6:

$$
3c = 15 + 6 = 21
$$

Step 2: Divide by 3:

$$
c = \frac{21}{3} = 7
$$

✔ Answer: $ c = 7 $

---

#### (e) $ \frac{r}{4} + 4 = 3 $

Step 1: Subtract 4:

$$
\frac{r}{4} = 3 - 4 = -1
$$

Step 2: Multiply both sides by 4:

$$
r = -1 \times 4 = -4
$$

✔ Answer: $ r = -4 $

---

#### (f) $ 4(m - 6) = 16 $

Step 1: Divide both sides by 4:

$$
m - 6 = \frac{16}{4} = 4
$$

Step 2: Add 6:

$$
m = 4 + 6 = 10
$$

✔ Answer: $ m = 10 $

---

BONUS (g) $ 4e + 5 = 14 + e $

This is a bit more complex. We need to get all variables on one side and constants on the other.

Step 1: Subtract $ e $ from both sides:

$$
4e - e + 5 = 14 \\
3e + 5 = 14
$$

Step 2: Subtract 5:

$$
3e = 14 - 5 = 9
$$

Step 3: Divide by 3:

$$
e = \frac{9}{3} = 3
$$

✔ Answer: $ e = 3 $

---

✔ Final Answers Summary:

#### Section A
(a) $ w = 6 $
(b) $ y = 11 $
(c) $ m = 7 $
(d) $ a = 30 $
(e) $ b = 200 $
(f) $ k = 7 $

#### Section B
(a) $ a = 3 $
(b) $ d = 3 $
(c) $ z = 4 $
(d) $ c = 7 $
(e) $ r = -4 $
(f) $ m = 10 $
(g) $ e = 3 $ (Bonus)

---

Let me know if you'd like this formatted as a printable worksheet or want explanations in simpler language!