Question

How many solutions does this equation have?






2+6x/2 = 3x + 3

Answer 1

To find how many solutions the equation \( \frac{2 + 6x}{2} = 3x + 3 \) has, we need to solve it step by step.

1. First, let's simplify the left side of the equation:
\[
\frac{2 + 6x}{2} = \frac{2}{2} + \frac{6x}{2} = 1 + 3x
\]

2. Now, the equation can be rewritten as:
\[
1 + 3x = 3x + 3
\]

3. Next, we will isolate the terms involving \(x\):
\[
1 + 3x - 3x = 3
\]
\[
1 = 3
\]

This statement \(1 = 3\) is a contradiction, which means that the original equation has no solutions.

Thus, the equation \( \frac{2 + 6x}{2} = 3x + 3 \) has **no solutions**.