# Thread: combining like terms and solving equation.

1. ## combining like terms and solving equation.

5x + 8 + 3x - x + 5 = 6x - 3

thank you

2. Originally Posted by Patience
5x + 8 + 3x - x + 5 = 6x - 3

thank you
I'm not quite sure what level of math this is, so I'll try to explain this as best as I can without babying you.

So all plain numbers can be combined right? 5+3-2+7... you just follow the PEMDAS rules you learned and add them all up. Well all the numbers that are multiplied by a variable like "x" can be combined in the same way. So if 2+3+4-5 = 4, then similarly 2x+3x+4x-5x=4x. So let's look at your problem.

5x+8+3x-x+5 = 6x-3 (1)

Let's call this (1) and let's combine all "like terms" on each side of the equals sign.

Starting with the left:

5x+8+3x-x+5 (Separate the terms with an "x" from the terms without one)

5x+3x-x+8+5 (Now you can simplify the x's and the plain numbers just like we talked about)

5x+3x-x = 7x and 8+5=13.

So the whole left hand side can be written as 7x+13.

7x+13 = 6x-3 (2) Let's call this two.

Now let's look at the right hand side.

6x-3. Well there's nothing more you can do there. You just have two terms, one with an "x" and one without. You're done! Now let's find out just what x is.

So I'm sure you're learned that whatever you do to one side of the equals sign, you have to do to the other. If you subtract 3 from the left, subtract three from the right. If you add one billion to the left, add one billion to the right.

Let's look at (2) again.

7x+13 = 6x-3. Now let's take away 6x from both sides.

7x+13 - 6x = 6x-3 - 6x. Now let's simplify both sides.

(7x-6x) + 13 = (6x-6x) -3

(1x) +13 = 0 - 3

x+13= -3 Almost there!

Can you finish it?

3. (7x-6x) + 13 = (6x-6x) -3

(1x) +13 = 0 - 3

x+13= -2 (How did u get -2?)

this is what I got

x + 13 = -3

x + (13-13) = -3 -13

x + 0 = -16

x = -16

4. 5x + 8 + 3x - x + 5 = 6x - 3

-> add up non x terms on the right hand side

5x + 3x - x +13 = 6x - 3

-> add up x terms on the right hand side

7x + 13 = 6x - 3

-> move 13 from the right hand side to the left hand side

7x = 6x - 16

-> move 6x from left hand side to right hand side

-------------- check ------------------------------

5(-16) + 8 + 3(-16) - (-16) + 5 = -99
6(-16) - 3 = -99

5. Originally Posted by Patience
(7x-6x) + 13 = (6x-6x) -3

(1x) +13 = 0 - 3

x+13= -2 (How did u get -2?)

this is what I got

x + 13 = -3

x + (13-13) = -3 -13

x + 0 = -16

x = -16
You're absolutely right! Sorry I made a typo on the last step. You have the right answer.