Question

Solve the following equation for xx. Express your answer in the simplest form. 3, left parenthesis, minus, 2, x, plus, 1, right parenthesis, equals, 2, left parenthesis, minus, 3, x, plus, 2, right parenthesis 3(−2x+1)= 2(−3x+2)

Answer 1

Let's solve the equation \( 3(-2x + 1) = 2(-3x + 2) \).

First, we will distribute on both sides:

1. Distributing on the left side:
\[
3(-2x) + 3(1) = -6x + 3
\]

2. Distributing on the right side:
\[
2(-3x) + 2(2) = -6x + 4
\]

Now the equation becomes:
\[
-6x + 3 = -6x + 4
\]

Next, we will try to isolate \( x \) by adding \( 6x \) to both sides:
\[
-6x + 6x + 3 = -6x + 6x + 4
\]
This simplifies to:
\[
3 = 4
\]

This is a contradiction. Since we end up with a statement that is not true, this indicates that there are no solutions for \( x \).

The final answer is that the equation has no solution.