Question

How do you solve `x- 30+ 3x - 75+ \frac { 1} { 2} x + 15= 180`?

Answer 1

See a solution process below:

Explanation:

First, group and combine the like terms on the left side of the equation.

`x + 3x + 1/2x - 30 - 75 + 15 = 180`

`1x + 3x + 1/2x - 30 - 75 + 15 = 180`

`(1 + 3 + 1/2)x + (-30 - 75 + 15) = 180`

`(4 + 1/2)x + (-105 + 15) = 180`

`([2/2 xx 4] + 1/2)x + (-90) = 180`

`(8/2 + 1/2)x - 90 = 180`

`(8 + 1)/2x - 90 = 180`

`9/2x - 90 = 180`

Next, add `color(red)(90)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`9/2x - 90 + color(red)(90) = 180 + color(red)(90)`

`9/2x - 0 = 270`

`9/2x = 270`

Now, multiply each side of the equation by `color(red)(2)/color(blue)(9)` to solve for `x` while keeping the equation balanced:

`color(red)(2)/color(blue)(9) xx 9/2x = color(red)(2)/color(blue)(9) xx 270`

`cancel(color(red)(2))/cancel(color(blue)(9)) xx color(blue)(cancel(color(black)(9)))/color(red)(cancel(color(black)(2)))x = 540/9`

`x = 60`