Algebra Linear Inequalities

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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.

Oct 14th, 2015

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.
Oct 14th, 2015

Thank you very much for your help. So the answer is just the linear inequality. Would it be all real numbers. I'm still confused about that. I'm sorry it takes me a couple times to get problems like this sometimes.

Oct 14th, 2015

no worries :-)

yes, they are all real numbers (

real numbers = any set of rational and/or irrational numbers, any positive or negative, any size, including decimals

Oct 14th, 2015

Ok thank you very much for the help! and being patient with me. Sometimes I have tons of quesions.

Oct 14th, 2015

questions are good... that's how we learn and get stuff straight in our heads :-)... 

so, question as much as you can and gain a bit of knowledge every time :-)

Oct 14th, 2015

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