Question

We can distribute the
4
1
​
to rewrite the left side of the equation without parentheses. What is (
4
1
​
·24x)+(
4
1
​
·36)?
4
1
​
(24x+36)
=
3(2x+3)

+
=
3(2x+3)

Answer 1

To rewrite the expression \( 41 \cdot (24x + 36) \) without parentheses and distribute \( 41 \) across the terms inside the parentheses, you perform the following steps:

1. Distribute \( 41 \) to \( 24x \):
\[
41 \cdot 24x = 984x
\]

2. Distribute \( 41 \) to \( 36 \):
\[
41 \cdot 36 = 1476
\]

3. Combine both results:
\[
41 \cdot (24x + 36) = 984x + 1476
\]

Now, you also have the expression on the right side of the equation, which is given as \( 3(2x + 3) \). If you want to rewrite this expression:

1. Distribute \( 3 \) across \( 2x \):
\[
3 \cdot 2x = 6x
\]

2. Distribute \( 3 \) across \( 3 \):
\[
3 \cdot 3 = 9
\]

3. Combine both results:
\[
3(2x + 3) = 6x + 9
\]

Now you have two expressions:
- Left side: \( 984x + 1476 \)
- Right side: \( 6x + 9 \)

If you want to set these two expressions equal to each other:
\[
984x + 1476 = 6x + 9
\]

If you were solving for \( x \), you can rearrange and solve this equation accordingly.