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

@Hero

Answer 2

My first impulse would be to re-write |x - 3| > 2 as
-2 > x - 3 > 2

but that would create a false conjunction, therefore, instead I split the conjunction into disjunctions and re-write it like this:

x - 3 > 2
x - 3 < -2

Now, I can solve for x for both inequalities from there.

Answer 3

x>5
x>1

Answer 4

x>5
x<1

It is important to pay attention to detail. There's a subtle difference between your solution and mine. Figure out why.

Answer 5

cause i had to flip the sign

Answer 6

would it be a conjuction then?

Answer 7

If you have to split it into two equations, it is a disjunction.

Answer 8

ok thanks