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Question 389529: Can you please help me on this question....
|-2x - 4| < 12
If x represents positive amounts in kilograms, what is the solution set?
Only positive integer solutions to the equation can be used and accepted.
How does this change the answer to the first question? Explain.
Found 2 solutions by haileytucki, robertb:
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! See if this helps you out a little
|-2x-4|<12
Remove the absolute value term. This creates a \ on the right-hand side of the equation because |x|=\x.
-2x-4<\(12)
Set up the + portion of the \ solution.
-2x-4<12
Move all terms not containing x to the right-hand side of the inequality.
-2x<16
Divide each term in the inequality by -2.
x>-8
Set up the - portion of the \ solution. When solving the - portion of an inequality, flip the direction of the inequality sign.
-2x-4>-(12)
Multiply -1 by the 12 inside the parentheses.
-2x-4>-12
Since -4 does not contain the variable to solve for, move it to the right-hand side of the inequality by adding 4 to both sides.
-2x>4-12
Subtract 12 from 4 to get -8.
-2x>-8
Divide each term in the inequality by -2.
-(2x)/(-2)<-(8)/(-2)
Simplify the left-hand side of the inequality by canceling the common factors.
x<-(8)/(-2)
Simplify the right-hand side of the inequality by simplifying each term.
x<4
The solution to the inequality includes both the positive and negative versions of the absolute value.
x>-8 and x<4
The solution is the set of values where x>-8 and x<4.
-8
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! The inequality |-2x-4| < 12 is the same as -12 < -2x-4 < 12.
-12 + 4 < -2x - 4 + 4 < 12+4, or -8 < -2x < 16, or 4 > x > -8, after division by -2.
For your first question, if POSITIVE amounts are required, then the solution set is 4 > x > 0.
For your second question, if we only want POSITIVE INTEGER solutions, the solution set is {1,2,3}.
Just keep 'em coming STUDENTS, it's for free...=D
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