Question

How do you solve `x- 0.5= 2( 0.3x - 0.2)`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`x - 0.5 = color(red)(2)(0.3x - 0.2)`

`x - 0.5 = (color(red)(2) xx 0.3x) - (color(red)(2) xx 0.2)`

`x - 0.5 = 0.6x - 0.4`

Next, add `color(red)(0.5)` and subtract `color(blue)(0.6x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(blue)(0.6x) + x - 0.5 + color(red)(0.5) = -color(blue)(0.6x) + 0.6x - 0.4 + color(red)(0.5)`

`-color(blue)(0.6x) + 1x - 0 = 0 + 0.1`

`(-color(blue)(0.6) + 1)x = 0.1`

`0.4x = 0.1`

Now/ divide each side of the equation by `color(red)(0.4)` to solve for `x` while keeping the equation balanced:

`(0.4x)/color(red)(0.4) = 0.1/color(red)(0.4)`

`(color(red)(cancel(color(black)(0.4)))x)/cancel(color(red)(0.4)) = 0.25`

`x = 0.25`