Wavy curve method the best way to solve inequalities….by Sailesh kumar sahu(BIT Durg, IIM Kozhikode)

Solve the inequality

Solution:Relax:- Inequalities is all about co-efficients of x and powers of x..so don’t panic..proceed..Here are some steps which you should follow while attempting such a question:-Step 1: Find the critical points of each term in the inequality.. For (x+3)…cp is -3( u just have to equate the term with 0 and find x) For (3x-2)…cp is 2/3.. so on

 Arrange the cps in the number line ..0 at middle –ve no.s at left and positive ones at rightStep 2:- Check the coefficient of x in each term:-1. (x+3)..here the coefficient is +ve.i.e +1..(note..dont bother about

coeffiecient..check the sign (+ve or –ve)2. (3x-2)2 ..again the coefficient is +ve3. Here x’s coefficient is negative.4. Same

Find the product of the coefficients..negative in this caseStep 3:- if the product of the coefficients is +ve then from the right side of the no. line, start the curve from top(since its positive) (if it would have been –ve u should start downwards..from –ve side) as in this case.

Step 4: now look at the power of x in the next term (next critical point)..as next cp is 2/3 which comes from (3x-2)5….and hence an odd power..so change the direction of curve..(keep the direction same if it would be an even power.)

Step 4b:-

Step 4c:- continue this step till u cover all critical points..(note : at point -8/5 no change will takes place as there is an even powered term (or we can say that power of x is even)..so there will be no change in direction..keep it as it is..

 

  

                                                 Fig (1)

            Step 5: if the inequality has >0 sign then consider the range which has a +ve curve

Similarly, if inequality has <0 sign then consider the range which has a –ve curve..

As the inequality in given case is >0 ..so we consider the above answer..

Pick any book and practice such questions..remember that procedure don’t change in questions where fractions exist..just divide the coefficients for a +ve or _ve result