Combining like Terms worksheets - Free Printable

To solve the given problems, we need to simplify each expression by combining like terms. Let's go through each problem step by step.

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Problem 1: \( 2x - 5x + 3 \)

- Combine the \( x \)-terms: \( 2x - 5x = -3x \)
- The constant term remains \( 3 \)
- Simplified expression: \( -3x + 3 \)

Answer: \( -3x + 3 \)

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Problem 2: \( (-3x) - 9 + 20x \)

- Combine the \( x \)-terms: \( -3x + 20x = 17x \)
- The constant term remains \( -9 \)
- Simplified expression: \( 17x - 9 \)

Answer: \( 17x - 9 \)

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Problem 3: \( 7x - 11 - 3x + 5 \)

- Combine the \( x \)-terms: \( 7x - 3x = 4x \)
- Combine the constant terms: \( -11 + 5 = -6 \)
- Simplified expression: \( 4x - 6 \)

Answer: \( 4x - 6 \)

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Problem 4: \( (-2)(9x + 1) - 8x \)

- Distribute \( -2 \): \( (-2)(9x) + (-2)(1) = -18x - 2 \)
- Combine with \( -8x \): \( -18x - 8x = -26x \)
- The constant term remains \( -2 \)
- Simplified expression: \( -26x - 2 \)

Answer: \( -26x - 2 \)

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Problem 5: \( 21x - 12x + 6 - 17 \)

- Combine the \( x \)-terms: \( 21x - 12x = 9x \)
- Combine the constant terms: \( 6 - 17 = -11 \)
- Simplified expression: \( 9x - 11 \)

Answer: \( 9x - 11 \)

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Problem 6: \( (-2)(6x - 2) + 6x \)

- Distribute \( -2 \): \( (-2)(6x) + (-2)(-2) = -12x + 4 \)
- Combine with \( 6x \): \( -12x + 6x = -6x \)
- The constant term remains \( 4 \)
- Simplified expression: \( -6x + 4 \)

Answer: \( -6x + 4 \)

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Problem 7: \( 4(1 + 5x) + 6x \)

- Distribute \( 4 \): \( 4(1) + 4(5x) = 4 + 20x \)
- Combine with \( 6x \): \( 20x + 6x = 26x \)
- The constant term remains \( 4 \)
- Simplified expression: \( 26x + 4 \)

Answer: \( 26x + 4 \)

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Problem 8: \( -x + 4(1 + 4x) \)

- Distribute \( 4 \): \( 4(1) + 4(4x) = 4 + 16x \)
- Combine with \( -x \): \( -x + 16x = 15x \)
- The constant term remains \( 4 \)
- Simplified expression: \( 15x + 4 \)

Answer: \( 15x + 4 \)

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Problem 9: \( -7x + 5y - 6x + 10y \)

- Combine the \( x \)-terms: \( -7x - 6x = -13x \)
- Combine the \( y \)-terms: \( 5y + 10y = 15y \)
- Simplified expression: \( -13x + 15y \)

Answer: \( -13x + 15y \)

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Problem 10: \( 10x - 3 + 45x \)

- Combine the \( x \)-terms: \( 10x + 45x = 55x \)
- The constant term remains \( -3 \)
- Simplified expression: \( 55x - 3 \)

Answer: \( 55x - 3 \)

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Problem 11: \( 7(1 + 10x) + 8(1 + 6x) \)

- Distribute \( 7 \): \( 7(1) + 7(10x) = 7 + 70x \)
- Distribute \( 8 \): \( 8(1) + 8(6x) = 8 + 48x \)
- Combine all terms: \( 7 + 8 + 70x + 48x = 15 + 118x \)
- Simplified expression: \( 118x + 15 \)

Answer: \( 118x + 15 \)

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Problem 12: \( 10(3 + 8k) - 8(k + 3) \)

- Distribute \( 10 \): \( 10(3) + 10(8k) = 30 + 80k \)
- Distribute \( -8 \): \( -8(k) + (-8)(3) = -8k - 24 \)
- Combine all terms: \( 30 + 80k - 8k - 24 = 30 - 24 + 80k - 8k = 6 + 72k \)
- Simplified expression: \( 72k + 6 \)

Answer: \( 72k + 6 \)

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Problem 13: \( 5(2x + 14) \)

- Distribute \( 5 \): \( 5(2x) + 5(14) = 10x + 70 \)
- Simplified expression: \( 10x + 70 \)

Answer: \( 10x + 70 \)

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Problem 14: \( (-5)(8x + 1) + 4(x + 2) \)

- Distribute \( -5 \): \( (-5)(8x) + (-5)(1) = -40x - 5 \)
- Distribute \( 4 \): \( 4(x) + 4(2) = 4x + 8 \)
- Combine all terms: \( -40x + 4x - 5 + 8 = -36x + 3 \)
- Simplified expression: \( -36x + 3 \)

Answer: \( -36x + 3 \)

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Final Answers:

1. \( -3x + 3 \)
2. \( 17x - 9 \)
3. \( 4x - 6 \)
4. \( -26x - 2 \)
5. \( 9x - 11 \)
6. \( -6x + 4 \)
7. \( 26x + 4 \)
8. \( 15x + 4 \)
9. \( -13x + 15y \)
10. \( 55x - 3 \)
11. \( 118x + 15 \)
12. \( 72k + 6 \)
13. \( 10x + 70 \)
14. \( -36x + 3 \)

\boxed{
\begin{aligned}
&1. -3x + 3 \\
&2. 17x - 9 \\
&3. 4x - 6 \\
&4. -26x - 2 \\
&5. 9x - 11 \\
&6. -6x + 4 \\
&7. 26x + 4 \\
&8. 15x + 4 \\
&9. -13x + 15y \\
&10. 55x - 3 \\
&11. 118x + 15 \\
&12. 72k + 6 \\
&13. 10x + 70 \\
&14. -36x + 3
\end{aligned}
}