Worksheet: Solving One-Step Equations using Addition and ... - Free Printable

It looks like you've uploaded a worksheet titled "Future USA Math Worksheet" with the topic: "Solving Two-Step Equations – Addition & Subtraction." The task is to:

1. Explain the Addition Property of Equality in your own words.
2. Solve each equation listed (from 1 to 13).

Let’s go through this step by step.

---

✔ 1. Explain the Addition Property of Equality

> The Addition Property of Equality states that if you add the same number to both sides of an equation, the two sides remain equal.

In other words, if
$$
a = b,
$$
then
$$
a + c = b + c
$$
for any number $ c $.

This property helps us solve equations by keeping the balance while isolating the variable.

---

✔ 2. Solve each equation

We’ll solve each two-step equation using inverse operations — mainly addition and subtraction — to isolate the variable.

---

#### (1) $ x + 7 = 15 $

Subtract 7 from both sides:
$$
x = 15 - 7 = 8
$$

✔ Answer: $ x = 8 $

---

#### (2) $ 2x - 12 = 14 $

Add 12 to both sides:
$$
2x = 14 + 12 = 26
$$

Now divide by 2:
$$
x = 26 ÷ 2 = 13
$$

✔ Answer: $ x = 13 $

---

#### (3) $ x - 4 = -3 $

Add 4 to both sides:
$$
x = -3 + 4 = 1
$$

✔ Answer: $ x = 1 $

---

#### (4) $ x + 9 = 29 $

Subtract 9 from both sides:
$$
x = 29 - 9 = 20
$$

✔ Answer: $ x = 20 $

---

#### (5) $ 3x + 4 = 19 $

Subtract 4 from both sides:
$$
3x = 19 - 4 = 15
$$

Divide by 3:
$$
x = 15 ÷ 3 = 5
$$

✔ Answer: $ x = 5 $

---

#### (6) $ 2x + y = 60 $

Wait — this has two variables, $ x $ and $ y $. But we only have one equation. Without more information, we cannot find unique values for both variables.

But perhaps it's meant to be a typo or miswritten? Let's double-check.

If it's supposed to be just one variable, maybe it's $ 2x + 4 = 60 $? Or $ 2x + 0y = 60 $? But as written, it's:

> $ 2x + y = 60 $

This is a linear equation with two variables — infinite solutions unless another equation is given.

But since this is a "Two-Step Equation" worksheet, likely it's a typo.

Let’s assume it was meant to be:
👉 $ 2x + 4 = 60 $ — common format.

Then:
$$
2x = 60 - 4 = 56 \Rightarrow x = 28
$$

But since it says $ 2x + y = 60 $, and no other info, we can't solve uniquely.

So let's proceed carefully.

But looking at the next problems, they are single-variable. So likely this is a mistake.

Alternatively, maybe it's asking for expression in terms of one variable?

But for now, we'll skip this and flag it.

✘ Problem (6): Not solvable with one equation and two variables.

But let's check the original image again.

Wait — in the image text, it says:

> (6) $ 2x + y = 60 $

Yes, so unless there's a typo, this is underdetermined.

But since it's a worksheet for two-step equations, probably intended to be:

👉 $ 2x + 4 = 60 $ or $ 2x + 10 = 60 $ — but as written, it's $ 2x + y = 60 $

So I will assume it's a typo and suppose it's $ 2x + 4 = 60 $ — a common problem.

But to be accurate, I’ll note the issue.

Let’s move on.

---

#### (7) $ 4x + 3 = 43 $

Subtract 3:
$$
4x = 40
$$

Divide by 4:
$$
x = 10
$$

✔ Answer: $ x = 10 $

---

#### (8) $ 2x + 5 = 25 $

Subtract 5:
$$
2x = 20
$$

Divide by 2:
$$
x = 10
$$

✔ Answer: $ x = 10 $

---

#### (9) $ 3x + 6 = 15 $

Subtract 6:
$$
3x = 9
$$

Divide by 3:
$$
x = 3
$$

✔ Answer: $ x = 3 $

---

#### (10) $ x - 150 = 40 $

Add 150:
$$
x = 40 + 150 = 190
$$

✔ Answer: $ x = 190 $

---

#### (11) $ 4x + 20 = 60 $

Subtract 20:
$$
4x = 40
$$

Divide by 4:
$$
x = 10
$$

✔ Answer: $ x = 10 $

---

#### (12) $ x - 10 = 10 $

Add 10:
$$
x = 20
$$

✔ Answer: $ x = 20 $

---

#### (13) $ x + 84 + (-2) = -20 $

First simplify:
$$
x + 84 - 2 = -20 \Rightarrow x + 82 = -20
$$

Subtract 82:
$$
x = -20 - 82 = -102
$$

✔ Answer: $ x = -102 $

---

#### (14) $ x + 12 = 67 $

Subtract 12:
$$
x = 67 - 12 = 55
$$

✔ Answer: $ x = 55 $

---

#### (15) $ -2x + 16 = -28 + 8 $

Simplify right side:
$$
-2x + 16 = -20
$$

Subtract 16:
$$
-2x = -20 - 16 = -36
$$

Divide by -2:
$$
x = (-36) / (-2) = 18
$$

✔ Answer: $ x = 18 $

---

🔍 Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ x = 8 $ |
| 2 | $ x = 13 $ |
| 3 | $ x = 1 $ |
| 4 | $ x = 20 $ |
| 5 | $ x = 5 $ |
| 6 | ✘ Not solvable (two variables, one equation) |
| 7 | $ x = 10 $ |
| 8 | $ x = 10 $ |
| 9 | $ x = 3 $ |
| 10 | $ x = 190 $ |
| 11 | $ x = 10 $ |
| 12 | $ x = 20 $ |
| 13 | $ x = -102 $ |
| 14 | $ x = 55 $ |
| 15 | $ x = 18 $ |

---

⚠️ Note on Problem (6)

Since $ 2x + y = 60 $ involves two variables, it cannot be solved uniquely without a second equation.

Possible interpretations:
- If it was meant to be $ 2x + 4 = 60 $, then $ x = 28 $
- If it was $ 2x + y = 60 $, then $ y = 60 - 2x $, which is a line of solutions.

But for a two-step equation worksheet, it's likely a typo.

---

✔ Final Answer:

Addition Property of Equality:
*If you add the same number to both sides of an equation, the equality remains true.*

Solutions:
1. $ x = 8 $
2. $ x = 13 $
3. $ x = 1 $
4. $ x = 20 $
5. $ x = 5 $
6. Not solvable (missing info)
7. $ x = 10 $
8. $ x = 10 $
9. $ x = 3 $
10. $ x = 190 $
11. $ x = 10 $
12. $ x = 20 $
13. $ x = -102 $
14. $ x = 55 $
15. $ x = 18 $

Let me know if you'd like a version of the worksheet with corrected problems!