Question

solve the inequality using wavy curve method
x(x-2)(x-5)/(x+3)^2(15-2x)^5<0

Answer 1

Answer:

The wavy curve method (also called the method of intervals) is a strategy used to solve inequalities of the form \frac{f(x)}{g(x)} > 0

g(x)

f(x)

>0 \left(<0, \, \geq 0, \, \text{or} \, \leq 0\right).(<0,≥0,or≤0). The method uses the fact that \frac{f(x)}{g(x)}

g(x)

f(x)

can only change sign at its zeroes and vertical asymptotes, so we can use the roots of f(x)f(x) and g(x)g(x) to sketch a graph of the function over different intervals