How do you solve $abs(7-2x)-8<3$ ?

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Answer 1 · 2016-12-03T21:03:54

$-2< x <9$

The given inequality is equivalent to:

$|7-2x|<11$

and then

$-11<7-2x<11$

You can subtract 7 and get:

$-18<-2x<4$

Since you'll multiply by -1, the inequality will be flipped:

$-4<2x<18$

At the end you can divide all the terms by 2 and get:

$-2< x <9$

How do you solve abs(7-2x)-8<3abs(7-2x)-8<3?