Worksheet displaying eight two-step equations to solve, including variables and constants, with options to expand and adjust difficulty.

Let's solve each of these two-step equations step by step. A two-step equation typically involves:

1. Isolating the variable term (by adding or subtracting),
2. Solving for the variable (by dividing or multiplying).

We'll go through each one.

---

a) $ 6p - 2 = 52 $

Step 1: Add 2 to both sides to eliminate the constant on the left:
$$
6p - 2 + 2 = 52 + 2 \\
6p = 54
$$

Step 2: Divide both sides by 6:
$$
p = \frac{54}{6} = 9
$$

✔ Answer: $ p = 9 $

---

b) $ 6y + 9 = 21 $

Step 1: Subtract 9 from both sides:
$$
6y + 9 - 9 = 21 - 9 \\
6y = 12
$$

Step 2: Divide by 6:
$$
y = \frac{12}{6} = 2
$$

✔ Answer: $ y = 2 $

---

c) $ 9d + 1 = 19 $

Step 1: Subtract 1:
$$
9d = 19 - 1 = 18
$$

Step 2: Divide by 9:
$$
d = \frac{18}{9} = 2
$$

✔ Answer: $ d = 2 $

---

d) $ 2x - 5 = 19 $

Step 1: Add 5 to both sides:
$$
2x = 19 + 5 = 24
$$

Step 2: Divide by 2:
$$
x = \frac{24}{2} = 12
$$

✔ Answer: $ x = 12 $

---

e) $ 6a - 1 = 41 $

Step 1: Add 1:
$$
6a = 41 + 1 = 42
$$

Step 2: Divide by 6:
$$
a = \frac{42}{6} = 7
$$

✔ Answer: $ a = 7 $

---

f) $ 4 = 4 + 4x $

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

Step 2: Divide by 4:
$$
x = 0
$$

✔ Answer: $ x = 0 $

---

g) $ 10 = 2m + 10 $

Step 1: Subtract 10 from both sides:
$$
10 - 10 = 2m \\
0 = 2m
$$

Step 2: Divide by 2:
$$
m = 0
$$

✔ Answer: $ m = 0 $

---

h) $ 3 + 8y = 99 $

Step 1: Subtract 3:
$$
8y = 99 - 3 = 96
$$

Step 2: Divide by 8:
$$
y = \frac{96}{8} = 12
$$

✔ Answer: $ y = 12 $

---

✔ Final Answers:

| Equation | Solution |
|--------|---------|
| a) $ 6p - 2 = 52 $ | $ p = 9 $ |
| b) $ 6y + 9 = 21 $ | $ y = 2 $ |
| c) $ 9d + 1 = 19 $ | $ d = 2 $ |
| d) $ 2x - 5 = 19 $ | $ x = 12 $ |
| e) $ 6a - 1 = 41 $ | $ a = 7 $ |
| f) $ 4 = 4 + 4x $ | $ x = 0 $ |
| g) $ 10 = 2m + 10 $ | $ m = 0 $ |
| h) $ 3 + 8y = 99 $ | $ y = 12 $ |

Let me know if you'd like a visual explanation or help checking any of them!