Question

How do you solve `\frac { 9} { 6} x + \frac { 5} { 3} = 4`?

Answer 1

`x=14/9`

Explanation:

The end goal is to solve for `x`, so we need to isolate the `x`.

Start by subtracting `5/3` on both sides, but to do that, we need to have common denominators, which in this case are `12`. So you need to change the fractions (still keeping the ratio) until the denominators are equal):

`9/6x+20/12=48/12`

Now you can subtract `20/12` from both sides:

`9/6x=28/12`

Multiply both sides by `6/9`:

`x=168/108`

Simplify:

`x=14/9`

Answer 2

`x=14/9`

Explanation:

If you are solving an equation which has fractions, you can get rid of them immediately by multiplying each term by the `LCD` (which is `color(blue)(6)` in this case.)

`9/6x +5/3 =4`

`(color(blue)(cancel6xx)9)/cancel6x +(color(blue)(cancel6^2xx)5)/cancel3 =color(blue)(6xx)4`

`9x +10 = 24" "larr` now solve as usual

`9x = 24-10`

`9x = 14`

`x = 14/9`

Note: A better approach would have been to simplify the first fraction to `3/2`, but the method and result is the same