How do you solve $2< \frac { 4x + 22} { x + 5} < 3$ ?

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Answer 1 · 2018-06-04T17:01:03

$4 < x <13$

$2<(4x+2)/(x+5)<3$

The ratio
$(4x+2)/(x+5)$
lies between 2 and 3

$(4x+2)/(x+5)>2$

$4x+2>2(x+5)$

$4x+2>2x+10$

$4x-2x>10-2$

$2x>8$

$x>4$

$(4x+2)/(x+5)<3$

$4x+2<3(x+5)$

$4x+2<3x+15$

$4x-3x<15-2$

$x<13$

$x>4, x<13$

$4 < x <13$

How do you solve 2< \frac { 4x + 22} { x + 5} < 32< \frac { 4x + 22} { x + 5} < 3?