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

this says the distance between \(x\) and 3 is greater than 2 units
so \(x\) could be more than 2 units to the right of 3 OR \(x\) could be more than 2 units to the left of 3

Answer 2

in math this means if you see \(|\text{something}|>p\)
you will end up with two intervals (an "or" statement)
whereas if you see \(|\text{something}|<p\) you will end up with one interval ( an "and" statement)

Answer 3

for the second part, to solve \(|x-3|>2\) solve the two inequalities
\[x-3>2\]
\[x-3<-2\] separately and get two separate intervals as your answer