Question

How do you solve `3>h/-2` and graph the solutions?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the inequality by `color(blue)(-2)` to solve for `h` 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 3 color(red)(<) color(blue)(-2) xx h/-2`

`-6 color(red)(<) cancel(color(blue)(-2)) xx h/color(blue)(cancel(color(black)(-2)))`

`-6 color(red)(<) h`

We can state the solution in terms of `h` by reversing or "flipping" the entire inequality:

`h > -6`

To graph this we will draw a vertical line at `-6` on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the right side of the line because the inequality operator contains a "greater than" clause:

graph{x>=-6 [-10, 10, -5, 5]}