How do I solve the polynomial inequality -6<=2(x-5)<7?

Apr 21, 2018

$2 \le x < \frac{17}{2}$

Explanation:

(1)$- 6 \le 2 \left(x - 5\right)$ and (2)$2 \left(x - 5\right) < 7$

(1):
$- 6 \le 2 x - 10$
$10 - 6 \le 2 x$
$4 \le 2 x$
$2 \le x$

(2)
$2 \left(x - 5\right) < 7$
$2 x - 10 < 7$
$2 x < 7 + 10$
$2 x < 17$
$x < \frac{17}{2}$

Result:
$2 \le x < \frac{17}{2}$