Question
\begin{tabular}{|l|l|}\hline 4) Simplify: \( 7 a+6-3 a-2 \) & 5) Simplify: \( 4(2 x-8)+3 y \) \\ \hline\end{tabular} \( \begin{array}{l}\text { Adapted from Illustrative Math } \\ \text { 2024-25 Uncommon Schools, Inc. All rights reserved. }\end{array} \) "The only way to learn mathematics is to do mathen
Ask by Henry Gough. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Simplify the expressions:
1. \(7a + 6 - 3a - 2 = 4a + 4\)
2. \(4(2x - 8) + 3y = 8x - 32 + 3y\)
Solution
Simplify the expression by following steps:
- step0: Solution:
\(7a+6-3a-2\)
- step1: Subtract the terms:
\(4a+4\)
Calculate or simplify the expression \( 4(2 x - 8) + 3 y \).
Simplify the expression by following steps:
- step0: Solution:
\(4\left(2x-8\right)+3y\)
- step1: Expand the expression:
\(8x-32+3y\)
Let's simplify the given expressions step by step.
### 4) Simplify: \( 7a + 6 - 3a - 2 \)
1. **Combine like terms**:
- Combine the terms with \(a\): \(7a - 3a = 4a\)
- Combine the constant terms: \(6 - 2 = 4\)
So, the simplified expression is:
\[
4a + 4
\]
### 5) Simplify: \( 4(2x - 8) + 3y \)
1. **Distribute the 4**:
- \(4 \cdot 2x = 8x\)
- \(4 \cdot (-8) = -32\)
2. **Combine the results**:
- The expression becomes \(8x - 32 + 3y\)
So, the simplified expression is:
\[
8x - 32 + 3y
\]
### Final Results:
- For \(7a + 6 - 3a - 2\), the simplified form is \(4a + 4\).
- For \(4(2x - 8) + 3y\), the simplified form is \(8x - 32 + 3y\).
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Extra Insights
To simplify \( 7a + 6 - 3a - 2 \), first combine like terms. You have \( 7a - 3a = 4a \) and \( 6 - 2 = 4 \). So, the simplified expression is \( 4a + 4 \)! For \( 4(2x - 8) + 3y \), start by distributing the 4: \( 8x - 32 + 3y \). There's no more like terms to combine, so the final simplified expression is \( 8x + 3y - 32 \). Happy simplifying!