Question
8. Bimplify eompletely, \[ \frac{3}{4}(16 m-8)+9 m \]
Ask by King Craig. in the United States
Dec 18,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
Simplify the expression:
\[
\frac{3}{4}(16m - 8) + 9m = 21m - 6
\]
Solution
To simplify the expression:
\[
\frac{3}{4}(16m - 8) + 9m
\]
follow these steps:
### Step 1: Distribute \(\frac{3}{4}\) to each term inside the parentheses
\[
\frac{3}{4} \times 16m + \frac{3}{4} \times (-8) + 9m
\]
### Step 2: Multiply the fractions
\[
\frac{3}{4} \times 16m = \frac{48m}{4} = 12m
\]
\[
\frac{3}{4} \times (-8) = \frac{-24}{4} = -6
\]
Now, substitute these back into the expression:
\[
12m - 6 + 9m
\]
### Step 3: Combine like terms
\[
12m + 9m - 6 = 21m - 6
\]
### Final Simplified Expression
\[
21m - 6
\]
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Extra Insights
To simplify the expression, first distribute \(\frac{3}{4}\) to the terms inside the parentheses: \[ \frac{3}{4}(16m) - \frac{3}{4}(8) + 9m \] Calculating each term gives: \[ 12m - 6 + 9m \] Now, combine the like terms (\(12m\) and \(9m\)): \[ (12m + 9m) - 6 = 21m - 6 \] So, the final simplified expression is: \[ 21m - 6 \]