Question

How do you graph the inequality `15>3z`?

Answer 1

See a solution process below:

Explanation:

First, we need to get the inequality in terms of `z`. Divide each side of the inequality by `color(red)(3)` to solve for `z` while keeping the inequality balanced:

`15/color(red)(3) > (3z)/color(red)(3)`

`5 > (color(red)(cancel(color(black)(3)))z)/cancel(color(red)(3))`

`5 > z`

Or, we can reverse or "flip" the inequality to state the solution in terms of `z`:

`z < 5`

To graph this we draw a vertical line at the point `5` on the horizontal axis.

The line will be a dashed line because the there is no "or equal to" clause in the inequality operator so the value `5` is not included in the solution set.

We we shade to the left of the line because the inequality operator is a "less than" clause.

graph{x<5}