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7(h+3)=6(h-3)

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2 Answers

          7(h + 3) = 6(h - 3)

Starting on the left hand side of the equation, distribute the 7 by multiplying it by each term inside the parenthesis (h + 3):

          7(h + 3) = 7·h + 7·3 = 7h + 21

Looking at the right hand side of the equation, distribute the 6 by multiplying it by each term inside the parenthesis (h - 3):

          6(h - 3) = 6·h - 6·3 = 6h - 18 

Now we arrive at the following:

          7(h + 3) = 6(h - 3)

          7·h + 7·3 = 6·h - 6·3

          7h + 21 = 6h - 18 

The goal is to solve for the unknown variable, h. To do so, we want to isolate it to one side of the equation by moving all term that contain this variable to one side of the equation and moving all other terms to the other side of the equation, combining like terms as we go. 

With this, we first subtract 6h from both sides of the equation and then subtract 21 from both sides of the equation:

          7h + 21 - 6h = 6h - 18 - 6h

         7h - 6h + 21 = 6h - 6h - 18

                1h + 21 = 0 - 18

                 h + 21 = - 18

          h + 21 - 21 = -18 - 21

                   h + 0 = -39

                         h = -39

Hi Annie - 

Are you trying to solve for h here?  If so, you first should simplify the equation:

7(h + 3) = 6(h - 3)  distribute here

7h + 21 = 6h - 18

Now move all of the terms containing h to one side and everything else to the other side (remember, you can do whatever you want to the equation as long as whatever you do to one side you do to the other).  So, to move all of the terms containing h to one side and everything else to the other, let's start by subtracting 6h from both sides:

(7h + 21) -6h = (6h - 18) - 6h

Rearranging a little and simplifying, we get:

7h - 6h + 21 = 6h - 6h - 18

h + 21 = -18

Now, let's subtract 21 from each side:

h + 21 - 21 = -18 - 21

h = -39 

Which is the final answer.  As a check, you can plug in this value for h in the original equation, and see if you get a true statement:

7(h + 3) = 6(h - 3)

7(-39 + 3) = 6(-39 - 3)

7(-36) = 6(-42)

-252 = -252

Since -252 does in fact equal -252, we know that we have the correct answer for h.  If we had the wrong answer for h, we would have something like -13 = 156 or something, which is not true.

Hope this helps!

Mike T.