hi guys,
can anyone help me to find my mistake, I can't figure out what's wrong, probably something small.
the correct answer should be -5<=x<=4
I got -1<=x<=4
cheers !
It's not so much a matter of a single "mistake" as that your whole concept is wrong! Do you understand that if x< y it does not necessarily follow that $\displaystyle x^2< y^2$? -3< 2 but 9 is NOT less than 4.
I would do this instead: solve the equation $\displaystyle \sqrt{x+ 5}- \sqrt{8- x}= 1$. Those points separate "<" and ">". Check one point in each interval to see if the the inequality is satisfied in that interval.