… "move the numbers so all like terms are on one side" sort of answer
Hello SB. I'd start the explanation by distinguishing between constant and variable terms. There are three terms, in the given equation.
-12 + z/3 = -6
z/3 is a variable term, and a pair of like-terms are the constants -12 and -6.
In general, the first steps in solving such equations are to separate variable terms from constant terms; that is, we collect all variable terms on one side of the equation and all constant terms on the other side. In this particular equation, it's easier to leave the variable term on the left-hand side and move that constant term to the right-hand side. (Otherwise, we'd need to move two terms, instead of one.)
Next, I'd remind
why we move like-terms to the same side: so we can combine them into a single term. (That's called 'simplifying'.) We move terms by adding their opposite -- we add that to each side. The opposite of -12 is 12. Therefore, we
add 12 to each side. On the left-hand side, the opposites 12 and -12 combine to make zero, so there's no longer a constant term on the left-hand side. On the right-hand side, we simplify, by adding the constants -6 and 12.
z/3 = 6
Lastly, I'd remind that 'solving for z' means finding the value of z that makes the original equation a true statement. I'd explain that our result above shows one-third of the solution -- it's 6. But, we're not interested in a third of the solution; we want the whole z. In other words, we want three times as much as what we see above. Therefore, we
multiply each side by 3, and we have solved for z.
z = 18
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