Question

How do you solve `\frac{3}{4} ( x + 2) - \frac{x}{5} \leq \frac{2}{5} ( 6- x ) + \frac{x}{4}`?

Answer 1

`x = 9/7`

Explanation:

We need to rearrange the equation to get `x <=` something.

For the sake of rearranging, we can treat the `<=` sign as an `=` sign.

`3/4(x+2)-x/5 <= 2/5(6-x) + x/4`

First we multiply everything by `4`

`3(x+2) - (4x)/5 <= 8/5(6-x) + x`

Then we take `x` from both sides

`3(x+2) - (4x)/5 -x <= 8/5(6-x)`

Then we add `(4x)/5` to both sides

`3(x+2) -x <= 8/5(6-x) + (4x)/5`

Then we expand the bracket on the left

`3x+6 -x <= 8/5(6-x) + (4x)/5`

Which is the same as

`2x+6 <= 8/5(6-x) + (4x)/5`

Then multiply everything by `5`

`5(2x+6) <= 8(6-x) + 4x`

Then we expand the brackets again, this time on both sides

`10x + 30 <= 48 - 8x + 4x`

Which is the same as

`10x + 30 <= 48 - 4x`

Now we add `4x` to both sides

`14x + 30 = 48`

Then we take `30` from both sides

`14x = 18`

Finally we divide both sides by `14`

`x = 18/14`

`x = 9/7`