Solving inequalities for absolute values

soulmate1

New member
Can someone please Help with this I am trying to help a friend in nursing school. Many thanks to anyone aho can help me with this....

I am not understanding when to graph as and or as or?

l0.6x-3l>0.6

pka

Elite Member
First make is simpler by dividing through by 0.6 :
$$\displaystyle \L\left| {0.6x - 3} \right| > 0.6\quad \Leftrightarrow \quad \left| {x - 5} \right| > 1$$.

Now solve these two inequalities:
$$\displaystyle \L x - 5 > 1\quad \text{or}\quad x - 5 < - 1$$.

soulmate1

New member
Thanks for the reply but what I am trying to find out is whats the rule for when to graph a solution as and or when to graph a solution as or?

jonboy

Full Member
You graph it on a number line. Say I have the solution set: x > 2 or x < -2.

You would draw your number line:

Code:
<--|--------|---------|-->
-2        0         2
Then since it's greater than 2 we have:

Code:
                     o------>
<--|--------|--------|-->
-2        0       2
With an open point because it's greater not equal.

Then we add the less than -2:

Code:
<-------o             o-------->
<--|------|------|-->
-2        0       2
Understand?

tkhunny

Moderator
Staff member
It almost never proves beneficial for this sort of third-person tutoring.

One very important thing to observe, when solving, graphing, manipulating, or just playing around, is how to make your life easier. This is what pka showed you. It was a massive step toward just what you are asking. If you see it as only a clue in the wrong direction, this conversation is not going to go well untill you upgrade some other skills.

The "rule" is to proceed in a rational and logical fashion.

In this case, there is simplicity.

Simply

1) Solve 0.6x - 3 = 0.6
2) Check which side of the solution "works".
3) Decide if you should included the end point.

sean39

New member
jonboy said:
...Say I have the solution set: x > 2 or x < -2.

(BTW there's no solution to this problem. You can't have a number greater than 2 and less than -2.)
If you are asked to solve a system of inequalities where x>2 and x<2, then it is true that there is no solution. In this case there is a solution by definition since you gave the solution set. The original problem that was posted here does have a solution set which is the union of the two disjoint sets that result from solving the inequality as described by pka.

tkhunny said:
1) Solve 0.6x - 3 = 0.6
2) Check which side of the solution "works".
3) Decide if you should include the end point.
Repeat the above three steps for 3 - 0.6x = 0.6

jonboy

Full Member
sean39 said:
If you are asked to solve a system of inequalities where x>2 and x<2, then it is true that there is no solution. In this case there is a solution by definition since you gave the solution set. The original problem that was posted here does have a solution set which is the union of the two disjoint sets that result from solving the inequality as described by pka.
You are right. Good catch and sorry for any confusion.