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

Jun 21, 2018

Let's solve each inequality for $h$:

First inequality:
$5 h + \left(- 4\right) \setminus \ge 6$

$\therefore 5 h - 4 \setminus \ge 6$

$\therefore 5 h \setminus \ge 10$

$\therefore h \setminus \ge 2$

Second inequality:
$7 h + 11 < 32$

$\therefore 7 h < 21$

$\therefore h < 3$

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.