Equivalent Algebraic Expressions Worksheets - Free Printable

Problem: Simplifying Algebraic Expressions

We are tasked with simplifying the given algebraic expressions. Let's solve each one step by step.

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#### 1) \( -6q + 7 - 2 + 4q \)

- Combine like terms:
- The \( q \)-terms: \( -6q + 4q = -2q \)
- The constant terms: \( 7 - 2 = 5 \)

- Simplified expression: \( -2q + 5 \)

Answer: \( -2q + 5 \)

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#### 2) \( 2b - 3b + 9 + 5 \)

- Combine like terms:
- The \( b \)-terms: \( 2b - 3b = -b \)
- The constant terms: \( 9 + 5 = 14 \)

- Simplified expression: \( -b + 14 \)

Answer: \( -b + 14 \)

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#### 3) \( -3(9b + 4) \)

- Distribute the \(-3\) across the terms inside the parentheses:
- \( -3 \cdot 9b = -27b \)
- \( -3 \cdot 4 = -12 \)

- Simplified expression: \( -27b - 12 \)

Answer: \( -27b - 12 \)

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#### 4) \( 9(8f + 3) - 7f \)

- Distribute the \(9\) across the terms inside the parentheses:
- \( 9 \cdot 8f = 72f \)
- \( 9 \cdot 3 = 27 \)

- Now, combine all terms:
- \( 72f + 27 - 7f \)
- Combine the \( f \)-terms: \( 72f - 7f = 65f \)
- The constant term remains \( 27 \)

- Simplified expression: \( 65f + 27 \)

Answer: \( 65f + 27 \)

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#### 5) \( 3 - 9h - 2 + 7h \)

- Combine like terms:
- The \( h \)-terms: \( -9h + 7h = -2h \)
- The constant terms: \( 3 - 2 = 1 \)

- Simplified expression: \( -2h + 1 \)

Answer: \( -2h + 1 \)

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#### 6) \( 3(5g - 7) - 8 \)

- Distribute the \(3\) across the terms inside the parentheses:
- \( 3 \cdot 5g = 15g \)
- \( 3 \cdot (-7) = -21 \)

- Now, combine all terms:
- \( 15g - 21 - 8 \)
- Combine the constant terms: \( -21 - 8 = -29 \)

- Simplified expression: \( 15g - 29 \)

Answer: \( 15g - 29 \)

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#### 7) \( -2(3 - 6r) \)

- Distribute the \(-2\) across the terms inside the parentheses:
- \( -2 \cdot 3 = -6 \)
- \( -2 \cdot (-6r) = 12r \)

- Simplified expression: \( 12r - 6 \)

Answer: \( 12r - 6 \)

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#### 8) \( 3q - 5 - 9q - 2 \)

- Combine like terms:
- The \( q \)-terms: \( 3q - 9q = -6q \)
- The constant terms: \( -5 - 2 = -7 \)

- Simplified expression: \( -6q - 7 \)

Answer: \( -6q - 7 \)

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#### 9) \( 6(-7 + 5y) - 9y \)

- Distribute the \(6\) across the terms inside the parentheses:
- \( 6 \cdot (-7) = -42 \)
- \( 6 \cdot 5y = 30y \)

- Now, combine all terms:
- \( -42 + 30y - 9y \)
- Combine the \( y \)-terms: \( 30y - 9y = 21y \)
- The constant term remains \( -42 \)

- Simplified expression: \( 21y - 42 \)

Answer: \( 21y - 42 \)

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#### 10) \( -8(7y + 6) \)

- Distribute the \(-8\) across the terms inside the parentheses:
- \( -8 \cdot 7y = -56y \)
- \( -8 \cdot 6 = -48 \)

- Simplified expression: \( -56y - 48 \)

Answer: \( -56y - 48 \)

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Final Answers:

\[
\boxed{
\begin{aligned}
1) & \ -2q + 5 \\
2) & \ -b + 14 \\
3) & \ -27b - 12 \\
4) & \ 65f + 27 \\
5) & \ -2h + 1 \\
6) & \ 15g - 29 \\
7) & \ 12r - 6 \\
8) & \ -6q - 7 \\
9) & \ 21y - 42 \\
10) & \ -56y - 48
\end{aligned}
}
\]