Question

How do you solve `x-2/3=-4/5`?

Answer 1

See the entire solution process below:

Explanation:

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

`color(red)(15)(x - 2/3) = color(red)(15) xx -4/5`

`(color(red)(15) xx x) - (color(red)(15) xx 2/3) = cancel(color(red)(15))3 xx -4/color(red)(cancel(color(black)(5)))`

`15x - (cancel(color(red)(15))5 xx 2/color(red)(cancel(color(black)(3)))) = -12`

`15x - 10 = -12`

Next, add `color(red)(10)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`15x - 10 + color(red)(10) = -12 + color(red)(10)`

`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`