Question

For the function R(x)= x+4/x-3, find the values of x that make the function less than or equal to 0

Answer 1

-4
`\leq`x<3

Explanation:

1)Break this into 2 case, equal to 0 and and less than 0.

2)The number equals zero if its numerator is 0 which happens when x=-4.

3) A fraction is less than 0 it is negative. Negative fractions are either +/- or -/+, so we have two subcases.

3a) For +/- the numerator is positive when x>-4 and denominator is negative when x<3. Putting those two together we have -4<x<3.

3b)For -/+ the numerator is negative when x<-4 and the denominator is positive when x>3 however those two values don't overlap.

4) Putting this together we have -4
`\leq`x<3