To rewrite the right side of the equation \( 2\frac{1}{2} (16x + 24) \) without parentheses, you need to distribute \( 2\frac{1}{2} \) (which is equivalent to \( \frac{5}{2} \)) to both terms inside the parentheses.
Here’s how you can do it step by step:
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Convert \( 2\frac{1}{2} \) to an improper fraction: \[ 2\frac{1}{2} = \frac{5}{2} \]
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Now, distribute \( \frac{5}{2} \) to each term in the expression \( 16x + 24 \): \[ \frac{5}{2} \cdot 16x + \frac{5}{2} \cdot 24 \]
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Perform the multiplication:
- For \( \frac{5}{2} \cdot 16x \): \[ \frac{5 \cdot 16x}{2} = \frac{80x}{2} = 40x \]
- For \( \frac{5}{2} \cdot 24 \): \[ \frac{5 \cdot 24}{2} = \frac{120}{2} = 60 \]
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Combine the results: \[ 2\frac{1}{2} (16x + 24) = 40x + 60 \]
Now you have the equation without parentheses: \[ 4(2x + 4) = 40x + 60 \]
So, \( 2\frac{1}{2} (16x + 24) \) rewritten without parentheses is \( 40x + 60 \).
Regarding the steps you provided, the appropriate actions to simplify \( 2\frac{1}{2} (16x + 24) \) are:
- Distribute \( 2\frac{1}{2} \) to the \( 16x \) and \( 24 \) (as we did above).
The other options (adding \( 24 \) or \( 16x \) to each side) are not necessary for this task of rewriting the right side without parentheses.
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