Question

Now, look at the right side. How could we rewrite the right side of the equation without parentheses so that it’s easier to work with?
4(2x+4)
=
2
1
​
(16x+24)

8x+16
=
2
1
​
(16x+24)

Add 24 to each side

Add 16x to each side

Distribute the
2
1
​
to the 16x and to the 24

Answer 1

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:

1. Convert \( 2\frac{1}{2} \) to an improper fraction:
\[
2\frac{1}{2} = \frac{5}{2}
\]

2. Now, distribute \( \frac{5}{2} \) to each term in the expression \( 16x + 24 \):
\[
\frac{5}{2} \cdot 16x + \frac{5}{2} \cdot 24
\]

3. Perform the multiplication:
- For \( \frac{5}{2} \cdot 16x \):
\[
\frac{5 \cdot 16x}{2} = \frac{80x}{2} = 40x
\]
- For \( \frac{5}{2} \cdot 24 \):
\[
\frac{5 \cdot 24}{2} = \frac{120}{2} = 60
\]

4. 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.