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

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Answer 1 · 2015-06-22T00:21:40

Split up the inequalities first

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

(2)
$7-2x<=3$
add $2x$ and subtract 3 on both sides:
$->4<=2x ->2 <= x$

(3)
Combining these:
$2<=x<4$

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