Question

We’re trying to make balanced moves to get closer to isolating x, but 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?
5(2x+4)=7x+3x+4

Subtract 5 from each side

Distribute the 5 to the 2x and to the 4

Divide both sides by 2x

Answer 1

To rewrite the left side of the equation \(5(2x + 4) = 7x + 3x + 4\) without parentheses, you should distribute the \(5\) to both terms inside the parentheses. Here's how you can do it:

1. **Distribute the 5**:
\[
5(2x) + 5(4) = 10x + 20
\]

So, the equation becomes:
\[
10x + 20 = 7x + 3x + 4
\]

Now, on the right side, we can combine like terms:
\[
10x + 20 = (7x + 3x) + 4 \implies 10x + 20 = 10x + 4
\]

Now the equation is easier to work with, as it is now \(10x + 20 = 10x + 4\). You can proceed to isolate \(x\) from here.

However, since both sides have \(10x\), you can subtract \(10x\) from both sides:
\[
20 = 4
\]

This statement is false, which implies that there are no solutions for \(x\) in the given equation. Thus, the original equation is inconsistent.