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

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Answer 1 · 2016-12-03T21:03:54

$- 2 < x < 9$ $-2< x <9$

The given inequality is equivalent to:

$| 7 - 2 x | < 11$ $|7-2x|<11$

and then

$- 11 < 7 - 2 x < 11$ $-11<7-2x<11$

You can subtract 7 and get:

$- 18 < - 2 x < 4$ $-18<-2x<4$

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

$- 4 < 2 x < 18$ $-4<2x<18$

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

$- 2 < x < 9$ $-2< x <9$

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