Question

How do you solve `x/.4 = 2x+1.2`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(0.4)` to eliminate the fraction while keeping the equation balanced:

`color(red)(0.4) xx x/0.4 = color(red)(0.4)(2x + 1.2)`

`cancel(color(red)(0.4)) xx x/color(red)(cancel(color(black)(0.4))) = (color(red)(0.4) xx 2x) + (color(red)(0.4) xx 1.2)`

`x = 0.8x + 0.48`

Next, subtract `color(red)(0.8x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`x - color(red)(0.8x) = 0.8x + 0.48 - color(red)(0.8x)`

`1x - color(red)(0.8x) = 0.8x - color(red)(0.8x) + 0.48`

`(1 - 0.8)x = 0 + 0.48`

`0.2x = 0.48`

Now, divide each side of the equation by `color(red)(0.2)` to solve for `x` while keeping the equation balanced:

`(0.2x)/color(red)(0.2) = 0.48/color(red)(0.2)`

`(color(red)(cancel(color(black)(0.2)))x)/cancel(color(red)(0.2)) = 2.4`

`x = 2.4`