Question
Inth ro Do, Hiesdy Coneco leghifesdy, com/student/dashboard/home Hane-caceponve Mow Thb Dushboard Home Practice: Equivalent Linear Expressions - Quiz - Leve e) Which expression is equivalent to \( 9\left(\frac{4}{3} m-5-\frac{2}{3} m+2\right) \) ? \( 6 m-27 \) \[ \frac{2}{3} m \] \( 18 m-27 \) \( 6 m+27 \)
Ask by Tran Bond. in the United States
Feb 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equivalent expression is \( 6m - 27 \).
Solution
Let's simplify the given expression step by step to find the equivalent expression.
**Given Expression:**
\[ 9\left(\frac{4}{3} m - 5 - \frac{2}{3} m + 2\right) \]
**Step 1: Simplify Inside the Parentheses**
Combine like terms:
\[
\frac{4}{3}m - \frac{2}{3}m = \frac{2}{3}m
\]
\[
-5 + 2 = -3
\]
So, the expression inside the parentheses becomes:
\[
\frac{2}{3}m - 3
\]
**Step 2: Distribute the 9**
Multiply each term inside the parentheses by 9:
\[
9 \times \frac{2}{3}m = 6m
\]
\[
9 \times (-3) = -27
\]
So, the expression simplifies to:
\[
6m - 27
\]
**Final Answer:**
\[ 6m - 27 \]
**Therefore, the correct option is:**
\[
\boxed{6m-27}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To simplify the expression \( 9\left(\frac{4}{3} m-5-\frac{2}{3} m+2\right) \), first, combine like terms inside the parentheses. You'll see that \( \frac{4}{3} m - \frac{2}{3} m = \frac{2}{3} m \) and \( -5 + 2 = -3 \). So it simplifies to \( 9\left(\frac{2}{3} m - 3\right) \). Distributing the 9 gives you \( 6 m - 27 \). So the equivalent expression is \( 6 m - 27 \). You can verify this by substituting different values for \( m \) and checking whether both expressions yield the same output! This kind of problem often appears on standardized tests, so practicing algebraic manipulations like this is a great way to sharpen your math skills!
