Question

How do you solve `5- \frac { 1} { 2} k > 0`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(5)` from each side of the inequality to isolate the `k` term while keeping the inequality balanced:

`-color(red)(5) + 5 - 1/2k > -color(red)(5) + 0`

`0 - 1/2k > -5`

`-1/2k > -5`

Now, multiply each side of the inequality by `color(blue)(-2)` to solve for `k` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`color(blue)(-2) xx 1/-2k color(red)(<) color(blue)(-2) xx -5`

`cancel(color(blue)(-2)) xx 1/color(blue)(cancel(color(black)(-2)))k color(red)(<) 10`

`1k color(red)(<) 10`

`k color(red)(<) 10`