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implify the following expressions. Write the strategy used bel \begin{tabular}{l|l}\( -3(x+4) \) & \( -2 a-3+4 a+8 \) \\ \( -3 x-12 \)\end{tabular}

Ask by Munoz Valdez. in the United States
Feb 23,2025

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Answer

Simplify the expressions using the distributive property and combining like terms. 1. –3(x + 4) simplifies to –3x – 12. 2. –2a – 3 + 4a + 8 simplifies to 2a + 5. Strategy: - Apply the distributive property where necessary. - Combine like terms to simplify each expression.

Solution

We are given two expressions to simplify. The strategy for both is to use the distributive property (if needed) and then combine like terms. 1. Expression: –3(x + 4)   • Use the distributive property: multiply –3 by x and –3 by 4.    –3 · x = –3x    –3 · 4 = –12   • Thus, the simplified expression is –3x – 12. 2. Expression: –2a – 3 + 4a + 8   • Group like terms: combine the a-terms and the constant terms.    a-terms: –2a + 4a = 2a    Constants: –3 + 8 = 5   • The simplified expression is 2a + 5. Summary of Strategy:   • Use the distributive property where necessary.   • Group and combine like terms. Final Answers:   –3(x + 4) simplifies to –3x – 12   –2a – 3 + 4a + 8 simplifies to 2a + 5

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The Deep Dive

To simplify the expression \( -3(x+4) \), we can use the distributive property, which states that \( a(b+c) = ab + ac \). So, we distribute \(-3\) to both \(x\) and \(4\): \[ -3(x+4) = -3 \cdot x - 3 \cdot 4 = -3x - 12 \] Now, let's simplify \( -2a - 3 + 4a + 8 \). Here, we combine like terms by grouping \(a\) terms together and constant terms together: \[ -2a + 4a + (-3 + 8) = (4a - 2a) + 5 = 2a + 5 \] So, our simplified expressions are: - For \( -3(x+4) \), the result is: \(-3x - 12\) - For \( -2a - 3 + 4a + 8 \), the result is: \(2a + 5\)

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