Find all real numbers $t$ such that $\frac{2}{3} t - 1 < t + 7 \le -2t + 15$. Give your answer as an interval.
+9488 23t−1<t+7≤−2t+15 Let's split it into two inequalities. 23t−1<t+7 −1−7<t−23t −8<13t −24<t and t+7≤−2t+15 t+2t≤15−7 3t≤8 t≤83 So t is greater than -24 but less than or equal to 8/3. t is in the interval:(−24,83]
+130475 (2/3)t - 1 < t+ 7 ≤ -2t + 15
First, we have
(2/3) t - 1 < t + 7 multiply through by 3
2t - 3 < 3t + 21 subtract 21, 2t from both sides
-24 < t
Then, we have
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......the answer is
(- 24, 8/3 ]
