Question

How do you solve `-3x + 8( 5x - 2) = - 275`?

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:

`-3x + color(red)(8)(5x - 2) = -275`

`-3x + (color(red)(8) xx 5x) + (color(red)(8) xx -2) = -275`

`-3x + 40x + (-16) = -275`

`-3x + 40x - 16 = -275`

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

`(-3 + 40)x - 16 = -275`

`37x - 16 = -275`

Then, add `color(red)(16)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`37x - 16 + color(red)(16) = -275 + color(red)(16)`

`37x - 0 = -259`

`37x = -259`

Now, divide each side of the equation by `color(red)(37)` to solve for `x` while keeping the equation balanced:

`(37x)/color(red)(37) = -259/color(red)(37)`

`(color(red)(cancel(color(black)(37)))x)/cancel(color(red)(37)) = -7`

`x = -7`

Answer 2

`x=-7`

Explanation:

`"distribute and simplify left side of equation"`

`-3x+40x-16=-275`

`rArr37x-16=-275`

`"add 16 to both sides"`

`37xcancel(-16)cancel(+16)=-275+16`

`rArr37x=-259`

`"divide both sides by 37"`

`(cancel(37) x)/cancel(37)=(-259)/37`

`rArrx=-7`

`color(blue)"As a check"`

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

`(-3xx-7)+8(-35-2)=21-296=-275`

`rArrx=-7" is the solution"`