# Thread: "Solving Equations with Variables on Both Sides"

1. ## "Solving Equations with Variables on Both Sides"

alright, heres the story. we had some homework assigned on the above subject, on a day i wasnt there. i missed the lesson, needless to say, and now have the weekend to learn it before a pretest. ive got a week to do the homework because i missed the day, but i still have to do the pretest. so, can someone give me a crash course on Solving Equations with Variables on Both Sides?

2. Ok let's say we have $\displaystyle 2x - 1 = 3x - 5$

Then let's try to get the x's and the numbers on different sides. In this case we will subtract the 2x from the left and right and add the 5 to the left and right then we will get our conclusion.

$\displaystyle 4 = x$ You can always plug that value back into the equation to make sure you got it right.

Here are a few others you can try.

$\displaystyle 5x + 1 = 8x - 8$
$\displaystyle 9x + 12 = 5x + 16$ (There's a little bit of a shortcut on this one see if you can notice it)
$\displaystyle 4x - 3 = 2x + 1$
$\displaystyle 11x + 20 = 13x - 10$

3. Originally Posted by SnipedYou
Ok let's say we have $\displaystyle 2x - 1 = 3x - 5$

Then let's try to get the x's and the numbers on different sides. In this case we will subtract the 2x from the left and right and add the 5 to the left and right then we will get our conclusion.

$\displaystyle 4 = x$ You can always plug that value back into the equation to make sure you got it right.

Here are a few others you can try.

$\displaystyle 5x + 1 = 8x - 8$
$\displaystyle 9x + 12 = 5x + 16$ (There's a little bit of a shortcut on this one see if you can notice it)
$\displaystyle 4x - 3 = 2x + 1$
$\displaystyle 11x + 20 = 13x - 10$

$\displaystyle 5x + 1 = 8x - 8$
subtract 5x from both sides, leaving 1 = 3x-8..
then add 8 to each side, leaving 9=3x, and divide each side by 3, which is 3=x
$\displaystyle 9x + 12 = 5x + 16$subtract 5x from both sides, 4x+12=16, subtract 12 from each side, leaving 4x=4, divide each side by 4, leaving x=1.
$\displaystyle 4x - 3 = 2x + 1$
subtract 2x from each side, leaving 2x-3 = 1
add 3 to each side, leaving 2x=4
divide each side by 2, x=2.
$\displaystyle 11x + 20 = 13x - 10$
subtract 11x from both sides..20=2x-10
Just so you know the shortcut I was getting at. Notice that $\displaystyle 9 + 12 = 5 + 16$ therefore x = 1. Its always good to check by solving though.