Question

First, let’s try to isolate the variable, x. Right now, x is inside the parentheses on the left. How could we rewrite the left side of the equation without parentheses so that it’s easier to work with?
2(4x+5)
=
10x+2

Distribute the 2 to the 4x and to the 5

Add 5 to each side

Add 2 to each side

Answer 1

To isolate the variable \( x \) in the equation you provided, we can start by correctly distributing the \( 2 \) to the terms inside the parentheses on the left side.

Starting with your expression:

\[
2(4x + 5)
\]

We will distribute the \( 2 \):

\[
2 \cdot 4x + 2 \cdot 5 = 8x + 10
\]

Now, your equation becomes:

\[
8x + 10 = 10x + 2
\]

Next, let's isolate the variable \( x \). We can start by simplifying the equation.

To eliminate \( 10x \) from the right side, we subtract \( 10x \) from both sides:

\[
8x + 10 - 10x = 10x + 2 - 10x
\]

This simplifies to:

\[
-2x + 10 = 2
\]

Next, we can isolate the term with \( x \) by subtracting \( 10 \) from both sides:

\[
-2x + 10 - 10 = 2 - 10
\]

This gives us:

\[
-2x = -8
\]

Finally, we can solve for \( x \) by dividing both sides by \( -2 \):

\[
x = 4
\]

So, the solution for \( x \) is \( 4 \).