Question

Consider the absolute value inequality |x - 3| > 2.
Part 1: Using complete sentences, explain whether this inequality will be an "and" compound inequality (conjunction) or an "or" compound inequality (disjunction) and why.
Part 2: Provide the solution to the inequality and describe the graph in complete sentences.

Answer 1

|x| = -x if x < 0
= x if x \(\ge\) 0

You can extend this to
|x-3| = -(x-3) if x-3 < 0
= x-3 if x-3 \(\ge\) 0

Answer 2

and take this further using the inequality

So you have to solve
x-3 > 2 and
-(x-3) > 2

Answer 3

what? you lost me.... :(

Answer 4

ok if you had |x-3| = 2, do you know how to solve that?

Answer 5

because then solving |x-3| > 2 is almost the same thing, but with minor details added

Answer 6

yea you add the three to the other side

Answer 7

hold on ill be back on in 15 mins

Answer 8

ok

Answer 9

What you wrote is partially correct. When you solve an absolute value, you are really solving 2 equations