Question

Let’s solve this equation step by step. You’re trying to get rid of the parentheses on the left by distributing the 1/2 to the 6x and to the 2
1/2(6x + 2) = 3x
? + ? = 3x

Answer 1

To solve the equation \( \frac{1}{2}(6x + 2) = 3x \) by distributing \( \frac{1}{2} \) to both terms inside the parentheses, we can break it down step by step:

1. Distribute \( \frac{1}{2} \) to \( 6x \):
\[
\frac{1}{2} \cdot 6x = 3x
\]

2. Distribute \( \frac{1}{2} \) to \( 2 \):
\[
\frac{1}{2} \cdot 2 = 1
\]

Now we can combine these results:
\[
3x + 1 = 3x
\]

At this point, the equation becomes:
\[
3x + 1 = 3x
\]

Next, we'll isolate the terms involving \( x \) to one side of the equation. We can subtract \( 3x \) from both sides:
\[
3x + 1 - 3x = 3x - 3x
\]
This simplifies to:
\[
1 = 0
\]

This indicates that there is no solution to the equation because it leads to a contradiction. In summary:
\[
\frac{1}{2}(6x + 2) = 3x \text{ results in } 1 = 0, \text{ which is false.}
\]
Thus, the original equation is not valid for any value of \( x \).