x/12 = 18

This one is easy.

When the variable x is divided by some number, we solve for x by multiplying both sides of the equation by that number.

Here's an example:

x/9 = 18

The variable x is divided by 9, so we solve by multiplying both sides by 9

9x/9 = 18 * 9

Now look at the lefthand side above. Do you see how the factor of 9 on top cancels with the 9 on the bottom, leaving just x?

x = 162

CHECK: Does 162 divided by 9 equal 18?

162/9 = 18

Yes, it does.

So x/9 = 18 means that x must be 162.

second problem is t/8 - 6 = 10

t/8 - 6 + 6 = 10 - 8

Your idea to add 6 to both sides is good because that will leave t/8 by itself on the lefthand side.

But, your work shows that you only added 6 to the lefthand side. Subtracting 8 from the righthand side is wrong.

__We must always do the same operation to both sides of an equation.__

:idea: That's a very basic rule of algebra! If we violate this rule by doing something *different* to each side, the two sides are probably no longer equal (that is, we've destroyed the equality, and our final answer will be wrong).

So, add 6 to BOTH sides

t/8 - 6 + 6 = 10 + 6

Next, simplify each side by doing the arithmetic.

In other words, -6 plus 6 is zero on the lefthand side, leaving t/8 by itself.

On the righthand side, you know how to simplify 10 + 6.

The last step is similar to your first exercise. t is divided by 8, so multiply BOTH sides by 8 and simplify (cancel the 8s) to finish.

PS: Don't forget to check your result for t, using the original equation.