How do you solve the compound inequality 3t-7>=5 and 2t+6<=12?

1 Answer

There are no values of $t$ that satisfy both inequalities.

Explanation:

We're looking for values of $t$ that satisfy both expressions. So let's solve both and see what we get:

$3 t - 7 \ge 5$

$3 t - 7 \textcolor{red}{+ 7} \ge 5 \textcolor{red}{+ 7}$

$3 t \ge 12$

$\frac{3 t}{\textcolor{red}{3}} \ge \frac{12}{\textcolor{red}{3}}$

color(blue)(tge4

$2 t + 6 \le 12$

$2 t + 6 \textcolor{red}{- 6} \le 12 \textcolor{red}{- 6}$

$2 t \le 6$

$\frac{2 t}{\textcolor{red}{2}} \le \frac{6}{\textcolor{red}{2}}$

color(blue)(tle3

Are there any values of $t$ that satisfy both inequalities? No, and so therefore there are no solutions to this system of inequalities.