Question

How do you solve and check your solution given `x-2/5=-8/15`?

Answer 1

See the entire solution and validation process below:

Explanation:

First, multiply each side of the equation by `color(red)(15)` to eliminate the fractions and keep the equation balanced:

`color(red)(15)(x - 2/5) = color(red)(15) xx -8/15`

`(color(red)(15) xx x) - (color(red)(15) xx 2/5) = cancel(color(red)(15)) xx -8/color(red)(cancel(color(black)(15)))`

`15x - (cancel(color(red)(15)) 3 xx 2/color(red)(cancel(color(black)(5)))) = -8`

`15x - 6 = -8`

Next, add `color(red)(6)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`15x - 6 + color(red)(6) = -8 + color(red)(6)`

`15x - 0 = -2`

`15x = -2`

Now, divide each side of the equation by `color(red)(15)` to solve for `x` while keeping the equation balanced:

`(15x)/color(red)(15) = -2/color(red)(15)`

`(color(red)(cancel(color(black)(15)))x)/cancel(color(red)(15)) = -2/15`

`x = -2/15`

To validate the solution we need to substitute `color(red)(-2/15)` back into the original equation for `color(red)(x)` and calculate the left side of the equation to ensure it equals `-8/15`:

`color(red)(x) - 2/5 = -8/15` becomes:

`color(red)(-2/15) - 2/5 = -8/15`

`color(red)(-2/15) - (3/3 xx 2/5) = -8/15`

`color(red)(-2/15) - 6/15 = -8/15`

`-8/15 = -8/15` therefore we have checked our solution.