y = -12
Step-by-step explanation:
Generally, the first step is to eliminate parentheses.
6y +42 = 2y -6
Now, you have a 3-step equation. I generally start by subtracting the variable term with the lowest coefficient. That leaves a variable term with a positive coefficient.
4y +42 = -6 . . . . . . subtract 2y from both sides (step 1)
Now, you want to eliminate the constant from the side of the equation that has the variable term. Add its opposite.
4y = -48 . . . . . . . . . add -42 to both sides (step 2)
Finally, you divide by the coefficient of the variable.
y = -12 . . . . . . . . . . divide both sides by 4 (step 3)
The solution is y = -12.
Additional comment
As you can see, the general approach is to obtain the variable on one side of the equation and a constant on the other side. You do this by performing the same math operation to both sides of the equation.
Here, we notice that the values outside parentheses are multiples of each other, so we can start by dividing by 2
3(y +7) = y -3 . . . . . . divide both sides by 2
3y +21 = y -3 . . . . . . . eliminate parentheses
Now, we can do steps 1 and 2 at the same time, by adding -21-y to both sides. This gets rid of unwanted variables and constants in one step. (Your teacher may want you to show separate steps.)
(3y +21) +(-21 -y) = (y -3) +(-21 -y)
2y = -24 . . . . . . . . . simplify
y = -12 . . . . . . . . . . . divide by the coefficient of the variable (step 3)
