#1**+3 **

\(\frac{2}{3} t - 1 < t + 7 \le -2t + 15 \)

We first have the inequality

2/3 t - 1 < t + 7 subtract 7 from both sides

2/3 t - 8 < t subtract 2/3 t from both sides

-8 < 1/3 t multiply both sides by 3

-24 < t

And we have the second inequalty

t + 7 ≤ -2t + 15 add 2t to both sides...subtract 7 from both sides

3t ≤ 8 divide both sides by 3

t ≤ 8/3

So (-24, 8/3 ] is the solution

CPhill
Apr 2, 2018