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?

Question

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 \( 4 \).