Question

How do you solve and graph `5h+ -4>=6` and `7h+11<32`?

Answer 1

Let's solve each inequality for `h`:

First inequality:
`5h+(-4)\ge 6`

`therefore 5h-4 \ge 6`

`therefore 5h \ge 10`

`therefore h \ge 2`

Second inequality:
`7h+11<32`

`therefore 7h < 21`

`therefore h < 3`

So, we are looking for all numbers that are more that `2` (included) but smaller than `3` (excluded).

To graph this on a number line, you can highlight the parte between `2` and `3`, pointing out in some way that `2` belongs to your set, while `3` doesnt.