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

we write the absolut value inequality as follows.....-2< x-3<2

Answer 2

or 1 < x< 5

Answer 3

The value of x lies between a and 5....therefore this inequality is a conjunction

Answer 4

x is greater than 1 and less than 5

Answer 5

I'm not sure about the conjunction and disjunction, but I think the solution 1<x<5 given by @sandyjayaram is not correct. For example, let's try plugging in x=2.
|x - 3| > 2
|2-3|>2
1>2
That is not true.

Answer 6

I think to get the solution, we can do it this way:
|x - 3| > 2
We first break up the absolute value inequality into:
(x-3)>2 and -(x-3)>2
Which simplifies into:
x-3>2 and -x+3>2
x>5 and 1>x
Thus those are the solutions.

Answer 7

I am sorry....i want to corect it

Answer 8

No problem @sandyjayaram , do you agree with my methodology?

Answer 9

yes i do

Answer 10

Nice. Kindly explain the conjunction and disjunction part if you can. I'm not sure about that.

Answer 11

ok...to find whether it is conjunction or disjunction we need to graph the solution

Answer 12

x < 1 , x >5 lets graph it