Question

Let's make balanced moves to get closer to isolating x. Right now, x is inside the parentheses on the left and right sides. Let’s start by looking at the left side. How could we rewrite the left side of the equation without parentheses so that it’s easier to work with?
1/4(24x+36)=3(2x+3)

Distribute the 1/4 to the 24x and to the 36

Divide both sides by 24x

Subtract 1/4 from each side

Answer 1

To rewrite the left side of the equation \( \frac{1}{4}(24x + 36) = 3(2x + 3) \) without parentheses, we can distribute \( \frac{1}{4} \) to both terms inside the parentheses. Let's do that step by step.

1. Distributing \( \frac{1}{4} \):
\[
\frac{1}{4}(24x) + \frac{1}{4}(36) = 6x + 9
\]
So we can rewrite the left side as \( 6x + 9 \).

2. The equation now looks like this:
\[
6x + 9 = 3(2x + 3)
\]

3. Next, we can distribute \( 3 \) on the right side:
\[
3(2x) + 3(3) = 6x + 9
\]

4. The equation simplifies to:
\[
6x + 9 = 6x + 9
\]

At this point, both sides of the equation are equal, and it indicates that they are equivalent for all \( x \). Thus, there’s no unique solution isolating \( x \) because every \( x \) satisfies the equation.

Let me know if you need further assistance or if you would like to explore a different problem!