Question

solve : x - 4/x + 3>0 where x is a real number and x is not equal to -3 and represent the solution set on real number line.​

Answer 1

Given:

 −3x≤2x−131<61

Taking L.C.M. of 3,2 and 6 is 6.

−3x×6≤2x×6−34×6<61×6

−2x≤3x−8<1

⇒−2x≤3x−8 and 3x−8<1

⇒8≤3x+2x     ⇒3x<1+8

⇒8≤5x        ⇒3x<9

⇒58≤x     ⇒x<3

∴ The solution set is {x:1.6≤x≤3,xϵR}