#### Answer

Hana must bowl at least 130 in the third game.
The solution set is {x|x $\geq$ 130}.

#### Work Step by Step

Let x represent the score in the third game.
Average for the three games = $\frac{144+176+x}{3}$
Because the average must be at least 150, we solve the following inequality.
$\frac{144+176+x}{3}$ $\geq$ 150
Multiply both sides by 3.
144 + 176 + x $\geq$ 450
320 + x $\geq$ 450
x $\geq$ 130
Hana must bowl at least 130 in the third game.
The solution set is {x|x $\geq$ 130}.