Question

How do you solve `2( 42- 2x ) + 2( 25- 2x ) = 500`?

Answer 1

See a solution process below:

Explanation:

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

`color(red)(2)(42 - 2x) + color(blue)(2)(25 - 2x) = 500`

`(color(red)(2) xx 42) - (color(red)(2) xx 2x) + (color(blue)(2) xx 25) - (color(blue)(2) xx 2x) = 500`

`84 - 4x + 50 - 4x = 500`

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

`84 + 50 - 4x - 4x = 500`

`(84 + 50) + (-4 - 4)x = 500`

`134 + (-8)x = 500`

`134 - 8x = 500`

Then, subtract `color(red)(134)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(134) + 134 - 8x = -color(red)(134) + 500`

`0 - 8x = 366`

`-8x = 366`

Now, divide each side of the equation by `color(red)(-8)` to solve for `x` while keeping the equation balanced:

`(-8x)/color(red)(-8) = 366/color(red)(-8)`

`(color(red)(cancel(color(black)(-8)))x)/cancel(color(red)(-8)) = -45.75`

`x = -45.75`