Question 992538
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what is solution for complex inequality of &nbsp;5 <2-3y <14
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The words &nbsp;"complex inequality" mean that there are, &nbsp;actually, &nbsp;two inequalities in one line. &nbsp;It is not about complex numbers, of course. 

By the way, &nbsp;this term &nbsp;"complex inequality" &nbsp;is not mathematically defined, &nbsp;and is not canonical. &nbsp;Simply speaking, &nbsp;this term is BAD, &nbsp;in my view. 

It would be better if you do not apply it.


Now let us solve it.


5 < 2-3y < 14. &nbsp;&nbsp;---> &nbsp;&nbsp;(distract 2 from both sides) &nbsp;&nbsp;--->


5-2 < -3y < 14-2,


3 < -3y < 12, &nbsp;&nbsp;---> &nbsp;&nbsp;(divide both sides by &nbsp;(-3)&nbsp; and change the inequality signs for opposites) &nbsp;&nbsp;--->


-1 > y > -4.


<U>Answer</U>. &nbsp;-4 < y < -1.