Let's break it down step-by-step.
- First, we start with the equation you have:
\[ \frac{1}{4}(24x + 36) = 3(2x + 3) \]
- 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:
\[ 3(2x + 3) = 3 \cdot 2x + 3 \cdot 3 = 6x + 9 \]
- Now we have:
\[ 6x + 9 = 6x + 9 \]
- By lying out the equation:
\[ 6x + 9 = 6x + 9 \]
- 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 \( x \).
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