Solve the nonlinear inequality. Express the solution using interval notation.

Question

x − 8 x + 6 ≥ 0

Answer 1

Let X = 8. Then X-8 = 0 and as long as the denominator not = 0 the solution will be 0 which is >= 0.

In this case any X >= 8 will solve the inequality.

There's another set of solutions.

When the numerator and denominator are both negative, the solution will be positive.

This happens for the first time when X = -7.

(-7 - 8) / (-7 + 6) = -15/-1 = +15 which is >= 0.

Thus, any X <= -7 will solve the inequality.

-infinity <= X <= -7 AND 8 >= X >= +infinity will both solve the problem.