Question

What is the solution set of the absolute value sentence
|x + 9| < 2?

Answer 1

Two principles can help here:
\[|a|^2=a^2\]and if\[a<b \text{ then }\]\[a^2<b^2 \text{ ; where }a,b>0\]

Answer 2

ok when have | | < or > any number
it will be come as:
-2< x+9< 2
then u jst has 2 let x alone by give -9 to both side
here it 'll be
-11< x< -7
thts it up to ths kind of question

Answer 3

now give me another ques if theres = insted of <

Answer 4

| | sign means "absolute value" meaning the sign inside the | | doesn't matter, it will always be positive.
for example;
|-9|=9
|9|=9
and you can solve this inequality just like solving equations.

Answer 5

x<-7

Answer 6

The | | sign does matter for inequalities. Not all x < -7 work, take -100 for example:
|-100+9|=|-91|=91. 91 is most definitely not less than 2.

Answer 7

\[\large{-2<x+9<2}\]now subtract 9 from both sides\[-11<x<-7\]

Answer 8

ohh I see, How did it become -2< x+9< 2 ???
I just want to know. :)

Answer 9

there is rule that if

where c should be positive

Answer 10

-2<x+9<2
-11<x<-7*this is the answer