Like Terms Teaching Resources :: 25 - 48 - Free Printable

You've uploaded an image containing a math worksheet titled “Combine Like Terms 1”, with instructions to “Solve for x.”

This is a standard algebra worksheet designed to practice combining like terms and solving linear equations.

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## ✔ How to Solve These Problems

Each equation has variable terms (with `x`) and constant terms (numbers). The goal is to:

1. Combine like terms on each side of the equation.
2. Isolate the variable `x` by moving all `x`-terms to one side and constants to the other.
3. Solve for `x` by dividing or multiplying as needed.

Let’s solve a few examples from the worksheet to demonstrate the method, then provide the full answer key.

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## 🔍 Example 1:
Equation: `3x + 22 - 14x = 0`

Step 1: Combine like terms

→ `3x - 14x + 22 = 0`
→ `-11x + 22 = 0`

Step 2: Isolate x

→ `-11x = -22`

Step 3: Solve for x

→ `x = (-22) / (-11)`
→ `x = 2`

✔ Answer: x = 2

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## 🔍 Example 2:
Equation: `2x + x - 30 = -36`

Step 1: Combine like terms

→ `3x - 30 = -36`

Step 2: Add 30 to both sides

→ `3x = -6`

Step 3: Divide by 3

→ `x = -2`

✔ Answer: x = -2

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## 🔍 Example 3:
Equation: `4x + 40 - 12x = -24`

Step 1: Combine like terms

→ `-8x + 40 = -24`

Step 2: Subtract 40 from both sides

→ `-8x = -64`

Step 3: Divide by -8

→ `x = 8`

✔ Answer: x = 8

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## 📋 Full Answer Key (All Problems Solved)

Here are the solutions for all 30 problems on the worksheet:

| Problem | Equation | Solution |
|---------|------------------------------|--------|
| 1 | 3x + 22 - 14x = 0 | x = 2 |
| 2 | 2x + x - 30 = -36 | x = -2 |
| 3 | 4x + 40 - 12x = -24 | x = 8 |
| 4 | 27x + 2x + 5x = 101 | x = 2.97 → Wait! Let's check: 34x = 101 → x = 101/34 ≈ 2.97 — but let’s keep exact fractions unless specified. Actually, 101 ÷ 34 = 101/34 (or ≈2.97). But perhaps we should check if it’s meant to be integer? Let’s recalculate: 27+2+5=34 → 34x=101 → x=101/34 → x = 101/34 (exact) |
| 5 | 4x + 16 - 6x = 11 | x = 2.5 → -2x = -5 → x = 5/2 = 2.5 |
| 6 | 14x + 50 - 4x = 8 | x = -4.2 → 10x = -42 → x = -4.2 or -21/5 |
| 7 | 2x - 8x + 26 = 50 | x = -4 → -6x = 24 → x = -4 |
| 8 | -44 + 4x + 15x = 51 | x = 5 → 19x = 95 → x = 5 |
| 9 | 4x + 20x + 40 = 8 | x = -1.6 → 24x = -32 → x = -4/3 ≈ -1.333... Wait — 24x = -32 → x = -32/24 = -4/3 |
| 10 | -79 - 4x + x = -13 | x = -22 → -3x = 66 → x = -22 |
| 11 | -69 + x - 7x = 3 | x = -12 → -6x = 72 → x = -12 |
| 12 | 10x + 3x - 60 = -2 | x = 4 → 13x = 58 → Wait! 13x = 58 → x = 58/13 ≈ 4.46 — Let me double-check: 10x+3x=13x; 13x - 60 = -2 → 13x = 58 → x = 58/13 |
| 13 | -81 + 21x = -1 | x = 80/21 ≈ 3.81 → 21x = 80 → x = 80/21 |
| 14 | 41 - 5x + 10x = 10 | x = -6.2 → 5x = -31 → x = -31/5 |
| 15 | 50 + 5x - 19x = 10 | x = 20/7 ≈ 2.857 → -14x = -40 → x = 40/14 = 20/7 |
| 16 | 3x + 6x - 60 = 4 | x = 64/9 ≈ 7.11 → 9x = 64 → x = 64/9 |
| 17 | 2x + 7x - 14x = 70 | x = -14 → -5x = 70 → x = -14 |
| 18 | 2x + x = -59 - 10 | x = -23 → 3x = -69 → x = -23 |
| 19 | 18 - x - 2x = 63 | x = -15 → -3x = 45 → x = -15 |
| 20 | 83 - 28x + 12x = -51 | x = 8.375 → -16x = -134 → x = 134/16 = 67/8 |
| 21 | 8x + 12x = 100 | x = 5 → 20x = 100 → x = 5 |
| 22 | -a + 4x = 0 | x = a/4 → This is unusual — probably typo? Maybe “-4 + 4x = 0”? If so, x = 1. But as written, it’s in terms of `a`. Assuming it’s a typo and meant `-4 + 4x = 0`, then x = 1. Otherwise, x = a/4. We’ll assume typo → x = 1 |
| 23 | -17x - 2x = -38 | x = 2 → -19x = -38 → x = 2 |
| 24 | -9x - 13x = -31 | x = 31/22 ≈ 1.409 → -22x = -31 → x = 31/22 |
| 25 | 23x + 15x = 42 | x = 1.105 → 38x = 42 → x = 42/38 = 21/19 |
| 26 | 85 - 2x - 3x = 40 | x = 9 → -5x = -45 → x = 9 |
| 27 | 91 + 17x - 4x = 78 | x = -1 → 13x = -13 → x = -1 |
| 28 | 2x - 87 - 7x = -15 | x = -14.4 → -5x = 72 → x = -72/5 |
| 29 | 16x - 13 - 36x = -13 | x = 0 → -20x = 0 → x = 0 |
| 30 | 50 + 11x - 28x = 70 | x = -20/17 ≈ -1.176 → -17x = 20 → x = -20/17 |

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## ⚠️ Note on Fractions and Decimals

Many answers are fractions. Unless the worksheet specifies rounding or decimal answers, it’s best to leave them as simplified fractions.

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## ✔ Final Answer Key (Simplified Fractions Where Applicable)

Here’s the clean, final answer key:

1. x = 2
2. x = -2
3. x = 8
4. x = 101/34
5. x = 5/2
6. x = -21/5
7. x = -4
8. x = 5
9. x = -4/3
10. x = -22
11. x = -12
12. x = 58/13
13. x = 80/21
14. x = -31/5
15. x = 20/7
16. x = 64/9
17. x = -14
18. x = -23
19. x = -15
20. x = 67/8
21. x = 5
22. x = 1 *(assuming typo: -4 + 4x = 0)*
23. x = 2
24. x = 31/22
25. x = 21/19
26. x = 9
27. x = -1
28. x = -72/5
29. x = 0
30. x = -20/17

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## 💡 Teaching Tip

When solving these, encourage students to:

- Always combine like terms first.
- Keep track of signs carefully.
- Check their answer by plugging it back into the original equation.

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✔ You now have the complete solution set for the worksheet “Combine Like Terms 1”. Let me know if you’d like a printable version or step-by-step walkthroughs for specific problems!