Solve: | 3 x + 4 | < 8 Give your answer as an interval.

Answer 1

|3x+4| < 8

-8 <3x+4 < 8

subtract 4

-12<3x <4

divide by 3

-4<x <4/3

(-4,4/3)

Answer 2

To make sure I don't error

I do this

let 3x+4=R

have two cases(two constraints)

1. R≥0 then solve R<8
2. R<0 then solve -R<8

each case must solve inequality (another constraint for each)

case 1. 3x+4≥0 so x≥-4/3

from equation x<4/3,,,,,valid interval for x is [-4/3,4/3)

case 2. 3x+4<0 so x<-4/3

from equation -3x-4<8,,,,,,,,,,,,x>-4,,,,,,,valid interval for x is (-4,-4/3)

x must be in interval (-4,4/3) which is [-4/3,4/3) union (-4,-4/3)