Inequalities using WAVY CURVE METHOD

Step -2 -> Value of x at which numerator becomes zero should be marked with dark circles.

Step – 3 -> All pints of discontinuities (x at which denominator becomes zero) should be marked on number line with empty circles. Check the value of f(x) for any real number greater than the right most marked number on the number line.

Step – 4 -> From right to left draw a wavy curve (beginnings above the number line in case of value of f(x) is positive in step–3 otherwise from below the number line), passing thoroughly all the marked points. So that when passes through a point (exponent whose corresponds factor is odd) intersects the number line, and when passing thoroughly a point (exponent whose corresponds factor is even) the curve doesn’t intersect the real line and remain on the same side of real line.

Step – 5 -> The appropriate intervals are chosen in accordance with the sign of inequality (the function f(x) is positive wherever the curve is above the number line, it is negative if the curve is found below the number line). Their union represents the solution of inequality

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