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

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Answer 1 · 2018-04-21T13:36:54

$2<=x<17/2$

(1) $-6<=2(x-5)$ and (2) $2(x-5)<7$

(1):
$-6<=2 x-10$
$10-6<=2x$
$4<=2x$
$2 <=x$

(2)
$2(x-5)<7$
$2 x-10<7$
$2 x < 7+10$
$2 x <17$
$x<17/2$

Result:
$2<=x<17/2$

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