Combinding Like Terms and Distributive Property Equations?

Question

I can't understand the math. I couldn't hear what the teacher said, and he didn't get to me before the bell rang so I have not clue about how to solve the problems. Heres one of them-2x+3-6x=10x+15-5
Can you help me with it? Thanks.

Answer 1

Combining like terms means that you separate each term based on whether it's a number or multiplied by a variable (in this case, x), and then combine the terms that have the exact same variable (or no variable).

2x + 3 - 6x= 10x + 15 - 5

Step 1: Rewrite so that all terms with x are on one side, and terms without x are on the other.
2x + 3 - 6x= 10x + 15 - 5

You can add the opposite of a term to both sides to move it, so:
(2x + 3 - 6x) - 10x = (10x + 15 - 5) - 10x
2x + 3 - 6x - 10x = 15 - 5
(2x + 3 - 6x - 10x) + 3 = (15 - 5) + 3
2x - 6x - 10x = 15 - 5 + 3

Step 2: Once like terms are together, you can combine them. The rule is that you can only combine terms that have the exact same variables, so you can combine 2x and 6x to get 8x, but not 2x^2 and 6x, or 2y and 6x.

Like normal, numbers that have no variable can also be combined, so 2 and 4 can be combined to get 6, but 2 and 4x cannot be combined.

2x - 6x - 10x = 15 - 5 + 3

2x - 6x - 10x = x(2 - 6 - 10) = -14x

15 - 5 + 3 = 13

Step 3: After combining like terms, solve.
-14x = 13
-14x / -14 = 13 / -14
x = -13/14 (solution!)