Question

How do you simplify `4x-2+(-6x)+8`?

Answer 1

See a solution process below for: 4x + 2 = 6x - 8

Explanation:

First, subtract `color(red)(4x)` and add `color(blue)(8)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`4x - color(red)(4x) + 2 + color(blue)(8) = 6x - color(red)(4x) - 8 + color(blue)(8)`

`0 + 10 = (6 - color(red)(4))x - 0`

`10 = 2x`

Now, divide each side of the fraction by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`10/color(red)(2) = (2x)/color(red)(2)`

`5 = (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))`

`5 = x`

`x = 5`

Answer 2

`4x-2+(-6x)+8=-2x+6`

Explanation:

First, since `4x-2=4x+(-2)`

We can say

`4x-2+(-6x)+8=4x+(-2)+(-6x)+8`

Then we group like terms

`4x+(-6x)+(-2)+8=(4x+(-6x))+((-2)+8)`

Then we simplify

`=(4x-6x)+(8-2)=(-2x)+(6)=ul(-2x+6)`