Question

We can distribute the
4
1
​
to rewrite the left side of the equation without parentheses. You can think of this as (
4
1
​
·24x)+(
4
1
​
·40). Rewrite the left side.
4
1
​
(24x+40)
=
2(3x+5)

+
=
2(3x+5)

Answer 1

To distribute \( 4 \) in the expression \( 4(24x + 40) \), we can do the following:

1. Multiply \( 4 \) by \( 24x \):
\[
4 \cdot 24x = 96x
\]

2. Multiply \( 4 \) by \( 40 \):
\[
4 \cdot 40 = 160
\]

Putting it all together, we rewrite the left side without parentheses:
\[
4(24x + 40) = 96x + 160
\]

Thus, the left side of the equation becomes:
\[
96x + 160
\]

Now, to complete the equation \( 4(24x + 40) = 2(3x + 5) \):
We first rewrite it fully as:
\[
96x + 160 = 2(3x + 5)
\]

Distributing \( 2 \) on the right side:
1. \( 2 \cdot 3x = 6x \)
2. \( 2 \cdot 5 = 10 \)

Thus, we have:
\[
96x + 160 = 6x + 10
\]

Putting all this together, we have:
\[
4(24x + 40) = 96x + 160
\]
and
\[
2(3x + 5) = 6x + 10.
\]

Hopefully, this clarifies the left side of your equation as you needed! If you have further questions or need help with any other part, feel free to ask!