Question

How do you solve `8-z/3>=11`?

Answer 1

`z<=-9`

Explanation:

We are given:

`8-z/3>=11`

Now, we can solve it with the following steps.

`-z/3>=11-8`

`-z/3>=3`

Multiplying by `3` on both sides, we get

`-z>=9`

We now need `z` instead of `-z`, so we divide by `-1`.

When dividing by a negative number, we must inverse the inequality sign.

`z<=-9`

Answer 2

See a solution process below:

Explanation:

First, subtract `color(red)(8)` from each side of the inequality to isolate the `z` term while keeping the inequality balanced:

`8 - color(red)(8) - z/3 >= 11 - color(red)(8)`

`0 - z/3 >= 3`

`-z/3 >= 3`

Now, multiply each side of the inequality by `color(blue)(-3)` to solve for `z` 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)(-3) xx -z/3 color(red)(<=) color(blue)(-3) xx 3`

`color(blue)(-3) xx z/-3 color(red)(<=) -9`

`cancel(color(blue)(-3)) xx z/color(blue)(cancel(color(black)(-3))) color(red)(<=) -9`

`z <= -9`