Question

John’s father is the head manager of a company that produces a best selling product. During the most recent computer upgrade, a new production inequality, |-2x - 4| < 12, was added to speed up production. The variable x in the inequality represents the amount of raw material (in kilograms) to make the product.
Solve the inequality. Show ALL work
If x represents positive amounts in kilograms, what is the solution set?

Answer 1

When you have an inequality of the form:

|expression in "x"| < a (with absolute value sign)

You have in essence:

-a < expression in "x" < a (without absolute value sign)

So, what needs to be done is to get your inequality into the second form, add 4 to all 3 parts, and lastly divide by "-2" and switch the direction of the inequality signs.

Answer 2

How are you doing with this so far? If you are stuck, just show me what you have done so far and then I can help you further. @feliveni

Answer 3

Thank you! Okay, so it's -8<x<4?

Answer 4

Excellent! Really good work! That's correct!

Answer 5

Thanks so much! One more thing-- If x represents positive amounts in kilograms, what is the solution set? ---Would that jhust be 0<x<4?

Answer 6

Yes, that's right. It cannot be:

0 <= x < 4

because if x is 0, then x is not positive, so you have represented the inequality correctly.

Answer 7

Awesome, thanks~

Answer 8

Good luck with all of your studies, you're welcome, and thx for the recognition! @feliveni