Question

How do you solve `14- 4k < 38`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(14)` from each side of the inequality to isolate the `k` term while keeping the equation balanced:

`14 - color(red)(14) - 4k < 38 - color(red)(14)`

`0 - 4k < 24`

`-4k < 24`

Now, divide each side of the inequality by `color(blue)(-4)` 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:

`(-4k)/color(blue)(-4) color(red)(>) 24/color(blue)(-4)`

`(color(red)(cancel(color(black)(-4)))k)/cancel(color(blue)(-4)) color(red)(>) -6`

`k color(red)(>) -6`

Answer 2

`k> -6`

Explanation:

We can treat this inequality like it's an equation. If our problem was instead `14-4k=38`, we would subtract `14` from both sides. We would do the same here to get:

`-4k<24`

Now, we divide both sides by `-4`, and here's the catch: Since we're dividing the inequality by a negative number, the direction of the sign will flip. This would even hold true of we're multiplying. We get:

`k> -6`

Answer 3

`k> -6`

Explanation:

`14-4k<38`

Start by subtracting `14` on both sides

`14 - 4k - 14 < 38 - 14`

`-4k < 24`

Divide both sides by `-4`
`(cancel(-4)k)/cancel(-4) < 24/(-4)`

`k > -6`

Note:

When you are solving an inequality, if you divide both sides by a negative sign, you MUST change the sign as well. If it was `<`, it will be `>`. Got it?