Expert: Richard J. Raridon - 7/16/2006

Question
(15 years old)
solve for X:
3x+6=9-2x
3x+6-2x=9-2x
3x+6-2x-5=9-2x+3
x/2+3x=10
x/2+3x+5=10
x/2+3+5=10-2x
x/2=3/5
x/2+5=3/5
x/2+3x=3/5
2/x=10
Manipulating An Equation
9+3q=25-q
7/x=3/6
t+2/3=9-t/4
4(4+r)=8r+2(r-10)
(2r)-4=5(8+4)r

Answer
Let's look at your first equation.
3x+6 = 9-2x
You can add or subtract a quantity from both sides of an equals sign without affecting the result.  So add 2x to each side to get 5x+6 = 9.  Now subtract 6 from each side to get 5x = 3.  You can also multiply or divide both sides by the same thing.  So divide both sides by 5 to get x=3/5.
Now look at x/2 +3x = 10.  Multiply each term by 2 to get
x +6x = 20 or 7x = 20.  Now divide both sides by 7 to get
x = 20/7.
for 7/x=3/6, multiply each side by 6 to get 42=3x or x=14.
Look at 4(4+r) = 8r+2(r-10)
First, multiply out the terms to get 16+4r = 8r+2r-20
Then combine terms to get 16+4r = 10r-20
so 36 = 6r and r = 6.
Now you can try the rest of them.