Question

How do you solve `(5x+6)/5 = (4x+10)/3`?

Answer 1

`-32/5`

Explanation:

Your goal here is to isolate `x` on one side of the equation.

To do that, start by finding the common denominator of the two fractions.

In this case, the least common multiple of `3` and `5` is `15`, which means that you will have to multiply the first fraction by `1 = 3/3` and the second fraction by `1 = 5/5` to get

`(5x+6)/5 * 3/3 = (4x+10)/3 * 5/5`

`(3(5x+6))/15 = (5(4x+10))/15`

At this point, you know that the equation comes down to

`3 * (5x+6) = 5 * (4x + 10)`

Expand the parantheses and isolate `x` on one side of the equation to get

`15x + 18 = 20x + 50`

`15x - 20x = 50 - 18`

`-5x = 32 implies x= color(green)(-32/5)`