Question 19333
Hello There:

3*(x - 6) + 6 = 5*(x + 2) - 12

(The asterisks mean multiplication.)

Start by using the distributive property to get rid of the parentheses.

3*(x - 6) means that both the x and the -6 inside of the parentheses gets multiplied by 3.  Likewise, both the x and the 2 get multiplied by 5 on the other set of parentheses.

3*x - 18 + 6 = 5*x + 10 - 12

Do the arithmetic on each side to add the constants together.

3*x - 12 = 5*x - 2

Next, we want all of the x-terms to be on one side of the equals sign and the constants on the other side.

Let's subtract 3*x from both sides.

3*x - 3*x - 12 = 5*x - 3*x - 2

-12 = 2*x - 2

Add 2 to each side.

2 - 12 = 2*x = 2 - 2

-10 = 2*x

Divide both sides by 2 to solve for x.

-10/2 = (2/2)*x

x = -5

Let's check our result.  We will substitute -5 for x into the original equation and simplify by doing the arithmetic to see if we end up with a true statement.

3*(x - 6) + 6 = 5*(x + 2) - 12

3*(-5 - 6) + 6 = 5*(-5 + 2) - 12

3*(-11) + 6 = 5*(-3) - 12

-33 + 6 = -15 - 12

-27 = -27

This is a true statement, so our solution is correct.

~ Mark