Question

Now that you've rewritten both sides of the equation without parentheses, take a look. How many solutions does this equation have?
1/4 (24x+36) = 3(2x+3)
6x+9 = 3(2x+3)
6x+9 = ? + ?

Answer 1

Let's break it down step-by-step.

1. First, we start with the equation you have:

\[
\frac{1}{4}(24x + 36) = 3(2x + 3)
\]

2. Now, we'll simplify both sides of the equation.

**Left Side:**

\[
\frac{1}{4}(24x + 36) = \frac{1}{4}(24x) + \frac{1}{4}(36) = 6x + 9
\]

**Right Side:**

\[
3(2x + 3) = 3 \cdot 2x + 3 \cdot 3 = 6x + 9
\]

3. Now we have:

\[
6x + 9 = 6x + 9
\]

4. By lying out the equation:

\[
6x + 9 = 6x + 9
\]

5. Notice that both sides of the equation are identical. This means that any value of \( x \) will satisfy this equation.

Thus, this equation has **infinitely many solutions** since it holds true for all values of \( x \).