Thread: combining like terms and solving equation.

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



I am very confused about this equation can someone explain this equation step by step please.


thank you

Originally Posted by Patience

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



I am very confused about this equation can someone explain this equation step by step please.


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?

(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

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

x = -16 ------> answer


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

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

therefore answer is correct

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.