Question

Please help!! I really don't understand this! Please explain answer!!

Identify the solution of the inequality (pretend the parentheses are absolute values) (x+3) -3 >(or equal to) 1.

x < -7
x > 1
x < -7 or x > 1
-7 < x < 1

Answer 1

$$ |x+3| - 3 \geq 1 $$

Bring over the -3
$$ |x+3| \geq 4 $$

Now we know that absolute value will make the value always positive. Be careful, x can be negative, zero, or positive, so we need to check all possibilities.

Answer 2

$$ |x+3| \geq 4 $$

We can try 0 right off the bat, and see that it does not work.

$$ |0+3| \geq 4 $$$$ \color{red}3 \color{red}\geq \color{red}4 $$ (not true)

Answer 3

Let's try the positive spectrum.
We know that if x=1, 1+3 = 4, so we can go ahead and conclude that if x is greater than or equal to 1, it will be greater than equal to 4
$$ |1+3| \geq 4 $$$$ |2+3| \geq 4 $$$$ |3+3| \geq 4 $$ ...etc.

Answer 4

What about negatives?
Well, it gets a bit tricky, but hopefully if I do it out you can see what I'm doing.

When the absolute value takes effect, we need the value to be -4 or less, meaning it needs to be -4, -5, -6, ... etc.

This is because when you do |-4| = 4, |-5| = 5, |-6| = 6 ... etc.

So, if you make x anything less than or equal to -7, (-7, -8, -9, etc.)

It will always produce a number less than or equal to -4. Then, when the absolute value is applied, $$|(-7)+3| \geq 4 \ \ \ \rightarrow\ \ \ |-4| \geq 4$$ $$|(-8)+3| \geq 4 \ \ \ \rightarrow\ \ \ |-5| \geq 4$$

Answer 5

Okay great thanks! I think I get that for the most part. But, what answer is it to my original problem?

Answer 6

Can you conclude it from the work I've done?
In order for x to be greater or equal to 4, what must it's range be?
Hint: It's a two part answer.

Answer 7

Is it the third answer?

Answer 8

Yes :)
Haha, I didn't even see the multiple choice answers you put in your question.

Answer 9

LOL! Thanks for all your help! Would you be willing to help me with one more question?

Answer 10

Unfortunately, it's 2am, and I have to head to bed. I have physics and Calc 3 tomorrow morning (well.. this morning). But feel free to post a new question! There should be plenty of people around to help. :)

Answer 11

Okay thanks! goodnight!