Question

How do you solve the equation `0.4 = (0.01 - x)/x` for `x`?

Answer 1

See the solution process below:

Explanation:

Step 1) Multiply each side of the equation by `color(red)(x)` to eliminate the fraction while keeping the equation balanced:

`0.4 * color(red)(x) = (0.01 - x)/x * color(red)(x)`

`0.4x = (0.01 - x)/color(red)(cancel(color(black)(x))) * cancel(color(red)(x))`

`0.4x = 0.01 - x`

Step 2) Add `color(red)(x)` to each side of the equation to isolate the `x` term while keeping the equation balanced;

`0.4x + color(red)(x) = 0.01 - x + color(red)(x)`

`0.4x + color(red)(1x) = 0.01 - 0`

`(0.4 + color(red)(1))x = 0.01`

`1.4x = 0.01`

Step 3) Divide each side of the equation by `color(red)(1.4)` to solve for `x` while keeping the equation balanced:

`(1.4x)/color(red)(1.4) = 0.01/color(red)(1.4)`

`(color(red)(cancel(color(black)(1.4)))x)/cancel(color(red)(1.4)) = 0.01/color(red)(1.4)`

`x = 0.007` rounded to the nearest thousandth.