Questions: Simplify the following expression. -3+7(a-3b-1)-4(10-a+2b)

Simplify the following expression. -3+7(a-3b-1)-4(10-a+2b)
Transcript text: Simplify the following expression. \[ -3+7(a-3 b-1)-4(10-a+2 b) \]
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Solution

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Solution Steps

To simplify the given expression, we need to distribute the constants across the terms inside the parentheses and then combine like terms. This involves applying the distributive property and then simplifying the resulting expression by combining terms with the same variables.

Step 1: Distribute Constants Across Parentheses

To simplify the expression \(-3 + 7(a - 3b - 1) - 4(10 - a + 2b)\), we first distribute the constants \(7\) and \(-4\) across the terms inside the parentheses:

\[ 7(a - 3b - 1) = 7a - 21b - 7 \]

\[ -4(10 - a + 2b) = -40 + 4a - 8b \]

Step 2: Combine Like Terms

Next, we combine all the terms from the expanded expression:

\[ -3 + 7a - 21b - 7 - 40 + 4a - 8b \]

Combine the like terms:

  • Constant terms: \(-3 - 7 - 40 = -50\)
  • Terms with \(a\): \(7a + 4a = 11a\)
  • Terms with \(b\): \(-21b - 8b = -29b\)
Step 3: Write the Simplified Expression

The simplified expression is:

\[ 11a - 29b - 50 \]

Final Answer

The expression simplifies to:

\[ \boxed{11a - 29b - 50} \]

The correct answer from the given options is the first one: \(11a - 29b - 50\).

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