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

Question

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 \( x \).