Question

Solve inequality |(x+3)^2|<1

Answer 1

The exponent is confusing me

Answer 2

get rid of the || first, its redundant

then square root?!

Answer 3

Let's solve your inequality step-by-step.
(x+3)2<1
x2+6x+9<1
Let's find the critical points of the inequality.
x2+6x+9=1
x2+6x+9−1=1−1(Subtract 1 from both sides)
x2+6x+8=0
(x+2)(x+4)=0(Factor left side of equation)
x+2=0 or x+4=0(Set factors equal to 0)
x=−2 or x=−4
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<−4(Doesn't work in original inequality)
−4<x<−2(Works in original inequality)
x>−2(Doesn't work in original inequality)
Answer:
−4<x<−2

Answer 4

so basically because of the exponent it's the same as |(x+3)|<1

Answer 5

yeahh

Answer 6

no

the square will be +ve so you don't need the | |, it's redundant so get rid of it first

Answer 7

yeahh thats what throws it off my fault

Answer 8

Casteil

try doing it yourself

having got rid of the ||, we can addresss the exponent directly and in far far fewer lines!!!

Answer 9

without the ||'s, what does the equation now say?

Answer 10

but square root of (x+3)^3 is again |x+3|

Answer 11

^2 not ^3

Answer 12

Right

Answer 13

if you know that
\((x+3)^2 < 1\)
then you know that \( |x+3|<1\), yes?

Answer 14

and then from that -1<x+3<1 and we get -4<x<-2

Answer 15

yes

Answer 16

well done castiel!