Two Step Equations - Math Worksheets - Free Printable

You’ve uploaded an answer key for a math worksheet titled “Two Step Equation - Integers.” The worksheet contains 12 two-step equations to solve, and the solutions are already shown with step-by-step work.

Since this is an answer key, the problems have already been solved correctly. However, I’ll walk you through how to solve each type of two-step equation using the examples provided, so you understand the method — not just the answers.

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## 🧠 General Strategy for Two-Step Equations

A two-step equation has the form:
> ax + b = c
or
> ax – b = c

To solve:
1. Undo addition or subtraction (isolate the term with the variable).
2. Undo multiplication or division (isolate the variable itself).

Always do the opposite operation on both sides of the equation.

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## ✔ Let’s Solve Each Equation Step-by-Step (Using First Row as Examples)

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🔹 Problem 1: `3x + 2 = 17`

Step 1: Subtract 2 from both sides to undo the "+2":
```
3x + 2 - 2 = 17 - 2
→ 3x = 15
```

Step 2: Divide both sides by 3 to undo the "×3":
```
3x ÷ 3 = 15 ÷ 3
→ x = 5
```

✔ Answer: x = 5

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🔹 Problem 2: `12 = 2y - 4`

Step 1: Add 4 to both sides to undo the "-4":
```
12 + 4 = 2y - 4 + 4
→ 16 = 2y
```

Step 2: Divide both sides by 2:
```
16 ÷ 2 = 2y ÷ 2
→ 8 = y or y = 8
```

✔ Answer: y = 8

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🔹 Problem 3: `4n - 7 = 1`

Step 1: Add 7 to both sides:
```
4n - 7 + 7 = 1 + 7
→ 4n = 8
```

Step 2: Divide by 4:
```
4n ÷ 4 = 8 ÷ 4
→ n = 2
```

✔ Answer: n = 2

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## 🔁 Apply Same Logic to All Problems

Let’s quickly verify one more from each row to confirm the pattern:

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🔹 Problem 4: `24 = 4 + 5x`

Subtract 4 → `20 = 5x` → Divide by 5 → `x = 4` ✔

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🔹 Problem 5: `26 = 5 - 3a`

Subtract 5 → `21 = -3a` → Divide by -3 → `a = -7` ✔

*(Note: When dividing by negative, sign flips)*

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🔹 Problem 6: `7 + 2c = 19`

Subtract 7 → `2c = 12` → Divide by 2 → `c = 6` ✔

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🔹 Problem 7: `6 + 3d = 18`

Subtract 6 → `3d = 12` → Divide by 3 → `d = 4` ✔

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🔹 Problem 8: `6n - 4 = 26`

Add 4 → `6n = 30` → Divide by 6 → `n = 5` ✔

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🔹 Problem 9: `-1 = 15 + 2b`

Subtract 15 → `-16 = 2b` → Divide by 2 → `b = -8` ✔

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🔹 Problem 10: `17 = 4y - 7`

Add 7 → `24 = 4y` → Divide by 4 → `y = 6` ✔

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🔹 Problem 11: `24 + 4z = -4`

Subtract 24 → `4z = -28` → Divide by 4 → `z = -7` ✔

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🔹 Problem 12: `-22 = -1 + 7d`

Add 1 → `-21 = 7d` → Divide by 7 → `d = -3` ✔

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## 📌 Summary of All Answers (From Answer Key):

| Equation | Solution |
|---------------------|----------|
| 3x + 2 = 17 | x = 5 |
| 12 = 2y - 4 | y = 8 |
| 4n - 7 = 1 | n = 2 |
| 24 = 4 + 5x | x = 4 |
| 26 = 5 - 3a | a = -7 |
| 7 + 2c = 19 | c = 6 |
| 6 + 3d = 18 | d = 4 |
| 6n - 4 = 26 | n = 5 |
| -1 = 15 + 2b | b = -8 |
| 17 = 4y - 7 | y = 6 |
| 24 + 4z = -4 | z = -7 |
| -22 = -1 + 7d | d = -3 |

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## 🎯 Key Takeaways

- Always isolate the variable term first (undo addition/subtraction).
- Then isolate the variable (undo multiplication/division).
- Check your answer by plugging it back into the original equation!
- Negative numbers are fine — just follow the rules of arithmetic carefully.

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✔ You now understand how to solve any two-step integer equation!
The worksheet’s answer key is correct, and the steps shown are accurate and complete.

Let me know if you’d like to practice similar problems or need help with word problems involving two-step equations!