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.

1. Solve the inequality. Show ALL work

2.If x represents positive kilograms, what's the solution set?

3.According to John’s father, only positive integer solutions to the equation can be used and accepted. How does this change the answer to question number 2?

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.

1.	Solve the inequality. Show ALL work

2.If x represents positive kilograms, what's the solution set?

3.According to John’s father, only positive integer solutions to the equation can be used and accepted.   How does this change the answer to question number 2?

anonymous · Answer

I've tried this on my own twice and got a 0 both times. Please help me before I pull my hair out . _ .''

kropot72 · Answer

anonymous · Answer

Then would the solution set for 2 be [-8,4]?

kropot72 · Answer

$$0< x \le 4$$

anonymous · Answer

(o,4} then :O So 3... how would I answer that? Just explain that there's no change because both are positive?

anonymous · Answer

ok lets make life easy and start with 
$$|2x+4|<12$$

anonymous · Answer

then remove the absolute value signs and get 
$$-12<2x+4<12$$subtract 4 and get 
$$-16<2x<8$$divide by 2 and get 
$$-8<x<4$$

anonymous · Answer

o - o ...so I was closer with [-8,4] but rather than the brackets I would just use parentheses, right?

anonymous · Answer

now we look closely and see that it says "x represents POSITIVE  kg so we get 
$$0\leq x \leq 4$$

anonymous · Answer

that is we are told that $x\geq 0$ to begin with

anonymous · Answer

My only remaining problem is with the third part of the question > _ <' How exactly would I go about wording the answer?

anonymous · Answer

so answer to question one is $[-8,4]$
answer to question 2 is $(0,4]$

anonymous · Answer

you know what positive integers are right?  
$\{1,2,3,4,5,...\}$

anonymous · Answer

so answer to question 3 is found by writing the positive integers that fall in the interval $(0,4]$

anonymous · Answer

So just list 0-4? o . o... I'm sorry, I'm not sure what it is but something about how that part of the question is worded twists my brain like a wet towel > _ >''