How do you solve x-5 < 7 - 2x <= 3?

Jun 22, 2015

Split up the inequalities first

Explanation:

(1)
$x - 5 < 7 - 2 x$
add 5 and add $2 x$ on both sides:
$\to 3 x < 12 \to x < 4$

(2)
$7 - 2 x \le 3$
add $2 x$ and subtract 3 on both sides:
$\to 4 \le 2 x \to 2 \le x$

(3)
Combining these:
$2 \le x < 4$