Question

the equation 3(2x + 1) = 4x + 2 - x has one solution. how can you tell? since one side has distribution and the other doesnt, the two sides dont match. each side has a different variable term, so the variables will not cancel each other out. each side has a different constant term, so they wont cancel out. there is 2x on the left and 4x on the right, so they dont match.

Explanation:

Step1: Simplify left - hand side

Use distributive property: $3(2x + 1)=6x+3$.

Step2: Simplify right - hand side

Combine like terms: $4x + 2−x=3x + 2$.

Step3: Analyze the simplified equation

The equation becomes $6x+3 = 3x+2$. Since the variable terms ($6x$ and $3x$) are different, the variables will not cancel each other out when solving for $x$. This means there is one solution for $x$.

Answer:

Each side has a different variable term, so the variables will not cancel each other out.