Question
Which expression is equivalent to \( (5 r t-3 r w-8 t w)+(6 r t-4 r w+2 t w) \) ? A. \( 11 r t+r w-10 t w \) B. \( 11 r t-7 r w-6 t w \) c. \( 11 r t+r w-6 t w \) D. \( 11 r t-7 r w-11 \) of 11
Ask by Gibson Klein. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equivalent expression is \( 11 r t - 7 r w - 6 t w \).
Solution
To simplify the expression \( (5 r t - 3 r w - 8 t w) + (6 r t - 4 r w + 2 t w) \), follow these steps:
1. **Combine like terms:**
- **\( r t \) terms:**
\[
5 r t + 6 r t = 11 r t
\]
- **\( r w \) terms:**
\[
-3 r w - 4 r w = -7 r w
\]
- **\( t w \) terms:**
\[
-8 t w + 2 t w = -6 t w
\]
2. **Combine the results:**
\[
11 r t - 7 r w - 6 t w
\]
**Therefore, the equivalent expression is:**
**B. \( 11 r t - 7 r w - 6 t w \)**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To simplify the expression \( (5 r t-3 r w-8 t w)+(6 r t-4 r w+2 t w) \), we first distribute and combine like terms: 1. Combine \( r t \): \( 5 r t + 6 r t = 11 r t \) 2. Combine \( r w \): \( -3 r w - 4 r w = -7 r w \) 3. Combine \( t w \): \( -8 t w + 2 t w = -6 t w \) Putting it all together, we have \( 11 r t - 7 r w - 6 t w \). So, the correct expression is option B: \( 11 r t - 7 r w - 6 t w \). Isn't it fun how combining like terms can lead you right to the answer? Just a little mathematical organization, and voilà!
