+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html)
+--- Forum: HP Prime (/forum-5.html)
+--- Thread: Result of an inequation, different from the algebraic process. (/thread-21733.html)
Result of an inequation, different from the algebraic process. - compsystems - 05-13-2024 02:18 AM
Hello
solve(((x-2)/(x+2))<2,x,'=') [ENTER] returns set[x<-6,x>-2] this is
(-2,+∞) union (-∞, -6)
but my calculations give me another domain.
(-2,+∞) union (-6,+∞)
Where am I going wrong?
step by step solution.
((x-2)/(x+2))<2
(x+2)>0
[(x+2)>0]+-2
(x+2-2)>(0-2)
(x+0)>-2
x>-2
(-2,+∞)
((x-2)/(x+2))<2
[((x-2)/(x+2))<2]*(x+2)
[((x-2)/(x+2))*(x+2)]<[2*(x+2)]
(x-2)<(2*x+4)
[(x-2)<(2*x+4)]+-2*x
[(x-2*x-2)<(2*x-2*x+4)]
(-x-2)<(4)
(-x-2+2)<(4+2)
(-x)<(6)
[-x<6]*-1
[-1*-x<6*-1]
(x)>(-6)
(-6,+∞)
Edit. a second case must be considered when the denominator is negative.
RE: Result of an inequation, different from the algebraic process. - Jan 11 - 05-13-2024 05:26 AM
Hi,
Hp Prime solves this inequality well. I solved the inequality on paper, manually, and got the same answer as Prime.
RE: Result of an inequation, different from the algebraic process. - parisse - 05-13-2024 06:11 AM
Move 2 to the left member, rewrite as a fraction, then replace / by * (this will not change sign),and find the sign of a polynomial of degree 2.