Question

I'm having trouble telling the difference between solution sets.
|-3x-12|>-24 Any clue?

Answer 1

when is an absolute value greater than a negative number?

Answer 2

is that a -24? or is that spose to be >= 24?

Answer 3

When it's positive. I understand somewhat what it is supposed to be but my professor is a bit confusing.
An problem like.: |-5x-10|>-30
That's \[(-\infty, \infty)\]
I need an explanation of why is this so.

Answer 4

Well rather, why infinity rather than numbers?

Answer 5

What's the solution to |x| = 0 ? It's x = 0.

Now for all x
\[ |x| \geq 0 \]

Hence if you have to solve
\[ |x| \geq 0 \]
that's all real numbers.

If you have
\[ |x-1| \geq 0 \]
that's satisfied by all real numbers

If you have for some arbitrary constant a
\[ |x-a| \geq 0 \]
that's satisfied by all real numbers.

Hence
\[ |x-a| \geq -1 \]
is also satisfied by all real numbers, as is
\[ |bx-a| \geq -1 \]

Now can you see why it's true for your inequality?

Answer 6

Well let me give you another one and maybe you might be able to explain a little more.
\[|2x-6|\ge0\]
The solution is \[(-\infty, \infty)\] As opposed to:
\[|3x-18|\ge0\] Where \[(-\infty, 6)u(6,\infty)\]
Why is this?

Answer 7

The solution to the second inequality is wrong.

\[ |3x - 18| \geq 0 \]
if and only if (iff)
\[ 3|x-6| \geq 0 \]
iff
\[ |x-6| \geq 0 \]
iff \( x \) is any real number.

Answer 8

This isn't my answer, this is my professors. I believe I am thinking the same way that you are but this is his way of doing it. He has taught for twenty some years so, I might have to sit down with him and have a conversation on this.

Answer 9

Ah, I know what the inequality is. You mean this:
\[ |3x - 18| > 0 \]
strictly greater than zero. Then 6 is not in the solution set.

Answer 10

Mm no its still

|3x−18|≥0

Answer 11

It is what he wrote on the blackboard.

Answer 12

Well, either he meant to write > or he's made an error in the solution.

Answer 13

I'm not entirely sure. Good part about this work is that it isn't graded at all so it wont affect my grade if I don't do them now. I will at least have the opportunity to sit down with him for a moment. I might try to get with him this Sunday afternoon because I know for a fact, Math isn't necessarily my strongest attribute, more of a literature/science guy. My test isn't for another week or so I have sometime. But thank you for helping me! I really appreciate you trying.