How do I solve this absolute value inequality? need help

Posted on 2015-09-02 06:04:00 in Math by MAYMUI

The problem is: 2 < -|3x-1|+3 <= 5 and someone told me the answer is no solution but I'm not sure how he got this. (If someone can confirm please show me how)

I know that you have to separate them, but first I'll subtract 3 on all sides, so

-1 < -|3x-1| <= 2

and then separate them,

-1 < -|3x-1| AND -|3x-1| <= 2

and then you have to assume both solutions of the absolute value, meaning one of them is negative.

BUT I'm not really sure how to do this since there is a negative in front of the absolute value. So do I divide by -1 to get rid of the negative in front of the absolute value (therefore flipping the signs)
i.e. 1>|3x-1| AND |3x-1 >= -2

or do I assume the two solutions first,
i.e. 1 < 3x-1 or -1 > 3x-1 AND 3x-1 <= 2 and 3x-1 >= -2

also, I could be wrong, but is the inequality -|3x-1| <= 2, no solution?

so my main to questions are, what is the answer to the problem and what do i do with the negative in front of the absolute value and how do I go about solving it? And can someone confirm if I'm right that -|3x-1| <= 2 is no solution and explain why.

THANK YOU SO MUCH. i have a huge test tomorrow and i'm still confused.

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