Friday

May 6, 2016
Posted by **chrissy** on Wednesday, August 1, 2007 at 7:43pm.

5x+12-3x=-2x-13-x x=-5

5x+12-3x=-2x-13-x

First, let's get the unknowns on one side of the equation and the knowns on the other side.

5x - 3x + 2x + x = -12 - 13

5 x = -25

x = - 5

ok I cant understand them the way you write them. I dont know how you got that or what you did to get it.

If you have as much money as me and we both get one dollar, then you'll still have as much money as I have.

If A is the amount of money you have and B is the amount of money I have and

A = B, then

A + 1 = B + 1

or in general:

A + C = B + C

for any number C.

If you take C to be minus B you get:

A - B = 0

So

A = B

implies that:

A - B = 0

This is called "bringing the term B to the other side".

In your problem, just bring all the x's to one side.

Ms. Sue moved all the x's on one side, the left side. When you do this, you have to change negatives into positives (or vice versa). She changed -2x into +2x when she moved it to the left of the equal sign. The same thing happened when she moved -x at the end of the original. It became +x. So she ended up with this on the left of the equal sign:

5x-3x+2x+x

She also had to move the whole numbers from the left side to the right side, again changing positive to negative. So now on the right side of the equal sign you have this:

-12-13

Then you simply do the math. How many positive x's do you have on the left? 5+2+1 (=8)

How many negative x's do you have on the left? -3

So 8x-3x = 5x

Do the same on the right side of the equal sign. -12-13 = -25

5x = -25

Divide both sides by 5 and you have your answer: x = -5

See??

Equations in algebra are made up of two sides. The equality exists and we can add, subtract, multiply, divide, or what have you, to one side IF we do it to the other side, too. For example,

2x - 7 = 7

We want to get the unknowns on one side (usually the left but that isn't necessary) and the numbers on the right. We can move the -7 on the left by adding +7 to BOTH sides of the equations, like so:

2x - 7 + 7 = 7 + 7

Now simplify, the -7 and +7 add to zero on the left (that's why we added 7 to both sides so it would cancel on the left) and we have 2x = 14. Then we want to know what 1x is so we divide both sides by 2 and we have

2x/2 = 14/2

x = 7.

A shortcut to adding and subtracting, which can be cumberson and inconvenient, is to simply move from one side to the other. To do that, we just change the sign; therefore, in the previous equation we had

2x - 7 = 7

we can simply move the -7 on the left to the right and change the sign when we do it so the equation becomes

2x = 7 + 7

2x = 14

etc.

Ms. Sue simply moved all the unknowns on the right to the left side and all the numbers on the left to the right side. She changed the sign when moving from one side to the other. Now, go through and see if that doesn't make sense to you.