I am having a very difficult time following this, but I think it's right. You are asked to solve
\(\displaystyle $6 y - 1 = 2 y + 2$\)
Just get y on one side, and do the same thing to both sides of the equation, until y is all by itself on that side. As soon as you get the variable you're solving for on a side by itself,
\(\displaystyle $4 y = 3$\)
\(\displaystyle $y = \frac{3}{4}$\)
you're done. So, stop solving, and plug your answer back in for the variable, to check your work:
\(\displaystyle $6 \cdot \frac{3}{4} - 1 = \frac{18}{4} - \frac{4}{4} = \frac{14}{4}$\)
and, the other side:
\(\displaystyle $2 \cdot \frac{3}{4} + 2 = \frac{6}{4} + \frac{8}{4} = \frac{14}{4}$\)
Now, since those two come out to the same thing, that means your answer's right. There is no "and then." If your answer were wrong, the original left-hand side of your equation would be NOT EQUAL to the original right-hand side of your equation.
