Question

What is the solution set of |2x + 4| < 8?

Answer 1

\[-8<2x+4<8\]

Answer 2

|2x-8| < 8
2x-8 < 8 or 2x-8 < -8
x-4 < 4 or x-4 < -4
x < 8 or x < 0 , hence x = (0, 8)

This comes from the definition of absolute value saying that |x| = -x if x<0 or |x| = x if x >= 0

Answer 3

"or" should be an "and" for intersection

Answer 4

kirby did you make a typo inside the abs value?

Answer 5

isn't it a union?

Answer 6

I always wrote "or" for these types of questions with absolute value inequalities o_O

Answer 7

-8<2x+4<8
-12<2x<4
-6<x<2
interval notation (-6,2)

Answer 8

Let k>0, k a real number, let r be a real number, then

|x - r| = k is equivalent to -(x-r)=k union x-r=k
|x - r| > k is equivalent to -(x-r)>k union x-r>k
|x - r| < k is equivalent to -(x-r)<k intersection x-r<k