Simplifying Algebraic Expressions worksheet with ten problems for practice.

Let's solve each of the algebraic expressions step by step. The goal is to simplify each expression by combining like terms and applying the distributive property where necessary.

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1) $-6q + 7 - 2 + 4q$

Combine like terms:
- Combine $-6q$ and $+4q$: $(-6 + 4)q = -2q$
- Combine constants: $7 - 2 = 5$

✔ Answer: $-2q + 5$

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2) $2b - 3b + 9 + 5$

Combine like terms:
- $2b - 3b = -b$
- $9 + 5 = 14$

✔ Answer: $-b + 14$

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3) $-3(9b + 4)$

Use the distributive property:
- $-3 \cdot 9b = -27b$
- $-3 \cdot 4 = -12$

✔ Answer: $-27b - 12$

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4) $9(6f + 3) - 7f$

First, distribute the 9:
- $9 \cdot 6f = 54f$
- $9 \cdot 3 = 27$

So: $54f + 27 - 7f$

Now combine like terms:
- $54f - 7f = 47f$
- Constant: $+27$

✔ Answer: $47f + 27$

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5) $3 - 9h - 2 + 7h$

Combine like terms:
- Constants: $3 - 2 = 1$
- Variables: $-9h + 7h = -2h$

✔ Answer: $-2h + 1$

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6) $3(5g - 7) - 8$

Distribute the 3:
- $3 \cdot 5g = 15g$
- $3 \cdot (-7) = -21$

So: $15g - 21 - 8$

Combine constants: $-21 - 8 = -29$

✔ Answer: $15g - 29$

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7) $-2(3 - 6r)$

Distribute the $-2$:
- $-2 \cdot 3 = -6$
- $-2 \cdot (-6r) = +12r$

✔ Answer: $12r - 6$

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8) $3q - 5 - 9q - 2$

Combine like terms:
- $3q - 9q = -6q$
- $-5 - 2 = -7$

✔ Answer: $-6q - 7$

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9) $6(-7 + 5y) - 9y$

Distribute the 6:
- $6 \cdot (-7) = -42$
- $6 \cdot 5y = 30y$

So: $-42 + 30y - 9y$

Combine like terms:
- $30y - 9y = 21y$

✔ Answer: $21y - 42$

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10) $-8(7y + 6)$

Distribute the $-8$:
- $-8 \cdot 7y = -56y$
- $-8 \cdot 6 = -48$

✔ Answer: $-56y - 48$

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✔ Final Answers:

1) $-2q + 5$
2) $-b + 14$
3) $-27b - 12$
4) $47f + 27$
5) $-2h + 1$
6) $15g - 29$
7) $12r - 6$
8) $-6q - 7$
9) $21y - 42$
10) $-56y - 48$

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Let me know if you'd like these written in a printable format or need help with any specific steps!