Algebra Worksheets - Free Printable

Let's solve each of these pre-algebra equations step by step using inverse operations. The goal is to isolate the variable $ y $ in each equation.

---

1. $ 3 + y \times 12 = 147 $

We need to isolate $ y $. First, subtract 3 from both sides:

$$
y \times 12 = 147 - 3 = 144
$$

Now divide both sides by 12:

$$
y = \frac{144}{12} = 12
$$

✔ Answer: $ y = 12 $

---

2. $ 8 \times y + y = 117 $

Combine like terms on the left:

$$
(8y + y) = 9y
$$

So:

$$
9y = 117
$$

Divide both sides by 9:

$$
y = \frac{117}{9} = 13
$$

✔ Answer: $ y = 13 $

---

3. $ 11^2 - 12 \times y = -47 $

First, compute $ 11^2 = 121 $

$$
121 - 12y = -47
$$

Subtract 121 from both sides:

$$
-12y = -47 - 121 = -168
$$

Divide both sides by -12:

$$
y = \frac{-168}{-12} = 14
$$

✔ Answer: $ y = 14 $

---

4. $ 10^2 - 12 \times y = 52 $

$ 10^2 = 100 $

$$
100 - 12y = 52
$$

Subtract 100 from both sides:

$$
-12y = 52 - 100 = -48
$$

Divide by -12:

$$
y = \frac{-48}{-12} = 4
$$

✔ Answer: $ y = 4 $

---

5. $ 11^2 - 10 \times y = -19 $

$ 11^2 = 121 $

$$
121 - 10y = -19
$$

Subtract 121:

$$
-10y = -19 - 121 = -140
$$

Divide by -10:

$$
y = \frac{-140}{-10} = 14
$$

✔ Answer: $ y = 14 $

---

6. $ 5 + 10 \times y = 155 $

Subtract 5 from both sides:

$$
10y = 155 - 5 = 150
$$

Divide by 10:

$$
y = \frac{150}{10} = 15
$$

✔ Answer: $ y = 15 $

---

7. $ 1^2 + y \times 10 = 151 $

$ 1^2 = 1 $

$$
1 + 10y = 151
$$

Subtract 1:

$$
10y = 150
$$

Divide by 10:

$$
y = 15
$$

✔ Answer: $ y = 15 $

---

8. $ 9 \times y + y = 60 $

Combine like terms:

$$
9y + y = 10y
$$

$$
10y = 60
$$

Divide by 10:

$$
y = 6
$$

✔ Answer: $ y = 6 $

---

9. $ 14 \times y + 14 = 224 $

Subtract 14 from both sides:

$$
14y = 224 - 14 = 210
$$

Divide by 14:

$$
y = \frac{210}{14} = 15
$$

✔ Answer: $ y = 15 $

---

10. $ 12^2 + y \times 10 = 164 $

$ 12^2 = 144 $

$$
144 + 10y = 164
$$

Subtract 144:

$$
10y = 164 - 144 = 20
$$

Divide by 10:

$$
y = \frac{20}{10} = 2
$$

✔ Answer: $ y = 2 $

---

✔ Final Answers:

1. $ y = 12 $
2. $ y = 13 $
3. $ y = 14 $
4. $ y = 4 $
5. $ y = 14 $
6. $ y = 15 $
7. $ y = 15 $
8. $ y = 6 $
9. $ y = 15 $
10. $ y = 2 $

Let me know if you'd like these steps written out in a worksheet format!