Question

How do you solve `1/ 2x - 2= 2( - x + 1)`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the equation:

`1/2x - 2 = (2 xx -x) + (2 xx 1)`

`1/2x - 2 = -2x + 2`

Next, multiply each side of the equation by `color(red)(2)` to eliminate the fraction while keeping the equation balanced:

`color(red)(2) xx (1/2x - 2) = color(red)(2) xx (-2x + 2)`

`(color(red)(2) xx 1/2x) - (color(red)(2) xx 2) = (color(red)(2) xx -2x) + (color(red)(2) xx 2)`

`x - 4 = -4x + 4`

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

`x - 4 + color(blue)(4) + color(red)(4x) = -4x + 4 + color(blue)(4) + color(red)(4x)`

`x + color(red)(4x) - 4 + color(blue)(4) = -4x + color(red)(4x) + 4 + color(blue)(4)`

`5x - 0 = 0 + 8`

`5x = 8`

Now, divide each side of the equation by `color(red)(5)` to solve for `x` while keeping the equation balanced:

`(5x)/color(red)(5) = 8/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 8/color(red)(5)`

`x = 8/5`