Question

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

Explanation:

Step1: Simplify left - hand side

Use distributive property $a(b + c)=ab+ac$. So, $3(2x + 1)=3\times2x+3\times1 = 6x+3$.

Step2: Simplify right - hand side

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

Step3: Analyze the simplified equation

The simplified equation is $6x+3 = 3x+2$. The variable terms are $6x$ and $3x$, and the constant terms are $3$ and $2$. An equation of the form $ax + b=cx + d$ ($a
eq c$) has one solution. Here, the variable terms on both sides are different ($6x
eq3x$), so the variables won't cancel each other out, and the equation has one solution.

Answer:

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