# equations

#### 2unique

##### New member
Could you please help me to figure this out. I have 2 problems.
I may already know how to do them , but can not remember.
first problem
x/12=18

second problem is t/8-6=10
on the second one i got this far
t/8-6+6=10-8
t=2
then i am lost or maybe I am just confused all the way around.

#### mmm4444bot

##### Super Moderator
Staff member
2unique said:
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.