Question

How do you solve `1/5 + (3x)/15=4/5`?

Answer 1

`x = 3`

Explanation:

Your ultimate goal is to isolate `x` on one side of the equation, so start by getting rid of the denominators.

Notice that you can multiply `1/5` and `4/5` by `1 = 3/3` to get

`1/5 * 3/3 + (3x)/15 = 4/5 * 3/3`

`3/15 + (3x)/15 = 12/15`

All the terms have the same denominator, which means that you can write

`(3 + 3x)/15 = 12/15`

`(3 + 3x) * color(red)(cancel(color(black)(1/15))) = 12 * color(red)(cancel(color(black)(1/15)))`

`3 + 3x = 12`

Next, add `-3` to both sides of the equation

`color(red)(cancel(color(black)(3))) - color(red)(cancel(color(black)(3))) + 3x = 12 -3`

`3x = 9`

Finally, divide both sides by `3` to get `x` alone on the left-hand side of the equation

`(color(red)(cancel(color(black)(3)))x)/color(red)(cancel(color(black)(3))) = 9/3`

`x = color(green)(3)`