Algebra Linear Inequalities

User Generated

WbfuVfGrpu

Mathematics

Description

Well I have the problem -15<2x-3<11 and I've gotten the answer -6<x<7 from working it out. My question is how do you know if it's all real numbers or if the linear inequality has no solution. Can someone please help me I'm stuck lol.

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Explanation & Answer

Thank you for the opportunity to help you with your question!

your answer to the equation is correct   -6 < x < 7

now, imaging these on a numbers line  -6--<--->---x---<--->---7  this is continuous, you defined an interval, saying that x is between -6 and +7

if the inequality would not have a solution, it would like something like x < -6 & x > 7

i.e.   --<---x--<--- -6     and  +7 ---->----x---   these do not overlap, are not continuous = no soln  

Please let me know if you need any clarification. I'm always happy to answer your questions.


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