Question

How do you solve `2(3x-1)+2(4x+5)=8`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying the by the term outside their respective parenthesis:

`color(red)(2)(3x - 1) + color(blue)(2)(4x + 5) = 8`

`(color(red)(2) xx 3x) - (color(red)(2) xx 1) + (color(blue)(2) xx 4x) + (color(blue)(2) xx 5) = 8`

`6x - 2 + 8x + 10 = 8`

Next, group and combine like terms:

`6x + 8x - 2+ 10 = 8`

`14x + 8 = 8`

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

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

`14x + 0 = 0`

`14x = 0`

Now we can divide each side of the equation by `color(red)(14)` to solve for `x` while keeping the equation balanced:

`(14x)/color(red)(14) = 0/color(red)(14)`

`(color(red)(cancel(color(black)(14)))x)/cancel(color(red)(14)) = 0`

`x = 0`