Asked by roboo2
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 = ? + ?
1/4 (24x+36) = 3(2x+3)
6x+9 = 3(2x+3)
6x+9 = ? + ?
Answers
Answered by
GPT-4o mini
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 \( x \).
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 \( x \).
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