Question

How do you solve `6x + 4( x - 2) = 14x - 8`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the term in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`6x + color(red)(4)(x - 2) = 14x - 8`

`6x + (color(red)(4) xx x) - (color(red)(4) xx 2) = 14x - 8`

`6x + 4x - 8 = 14x - 8`

`(6 + 4)x - 8 = 14x - 8`

`10x - 8 = 14x - 8`

Next, subtract `color(red)(10x)` and add `color(blue)(8)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(10x) + 10x - 8 + color(blue)(8) = -color(red)(10x) + 14x - 8 + color(blue)(8)`

`0 - 0 = (-color(red)(10) + 14)x - 0`

`0 = 4x`

Now, divide each side of the equation by `color(red)(4)` to solve for `x` while keeping the equation balanced:

`0/color(red)(4) = (4x)/color(red)(4)`

`0 = (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))`

`0 = x`

`x = 0`