Question

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

Answer 1

See a solution process below:

Explanation:

First, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

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

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

`6x + 16 + 2x - 2 = 4x + 32`

Next, group and combine like terms on the left side of the equation:

`6x + 2x + 16 - 2 = 4x + 32`

`(6 + 2)x + (16 - 2) = 4x + 32`

`8x + 14 = 4x + 32`

Then, subtract `color(red)(14)` and `color(blue)(4x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`8x - color(blue)(4x) + 14 - color(red)(14) = 4x - color(blue)(4x) + 32 - color(red)(14)`

`(8 - color(blue)(4))x + 0 = 0 + 18`

`4x = 18`

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

`(4x)/color(red)(4) = 18/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 9/2`

`x = 9/2`