Question

How do you solve `(-x+8)/(x-2)>=5`?

Answer 1

`x<=3`

Explanation:

If we start with `(-x+8)/(x-2)>=5`, then our first step should be to get rid of the denominator. To do that, we multiply both sides by `(x-2)`. That changes the eqaution into `(-x+8)/cancel(x-2)>=5*(x-2)`. If we distribute the `5`, it becomes `-x+8>=5x-10`. Just add `x` and `10` on both sides, and we are left with `18>=6x`. Divide by `6` on each side, and we see that `3>=x`. The conventional way to write inequalities is to have the variable first, so we shouls rewrite it as `x<=3`