Question 767013: The absolute value of (4x+1)/(x+2) is less than or equal to 3.
I got 5 and -2 as the critical numbers on (4x+1)/(x+2)<=3 and -1 and -2 on (4x+1)/(x+2)>=3. I also got the intervals (-2,5] and (-infinity, -2) or [-1, +infinity). I am not certain whether these are correct, and if ever they are, I do not know what to do after that. Can you please tell me what to do? Thank you very much, it would mean a lot to me.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! we use the pattern for less than and eliminate the absolute value by
solving two inequalities
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a) (4x+1) / (x+2) < or = 3
4x+1 < or = 3x+6 multiply both sides by x+2
x+1 < or = 6 subtract 3x from both sides
x < or = 5 subtract 1 from both sides
critical numbers are -2 and -1/4
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b) - (4x+1) / (x+2) < or = 3
(4x+1) / (x+2) > or = -3 multiply by -1
4x+1 > or = -3x-6 multiply by (x+2)
x+1 > or = -6 add -3x
x > or = -7 subtract -1
critical numbers are -2 and -1/4
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[-7,-2) and (-2, 5]
and 0 at -1/4
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