Question

Please Solve

Solve the following inequality. (x-4)(x + 1)(x-6)220 Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution". (0,0) [0,0] (0,0] [0,0) OVO No 8 solu

Answer 1

To solve the inequality (x-4)(x + 1)(x-6) ≥ 220, set up the inequality as a quadratic equation, find the critical points, and use them to determine the solution set.

Step-by-step explanation:

To solve the inequality (x-4)(x + 1)(x-6) ≥ 220, we can start by setting up the inequality as a quadratic equation:

(x-4)(x + 1)(x-6) - 220 ≥ 0

Next, we can find the critical points by setting the equation equal to 0:

(x-4)(x + 1)(x-6) - 220 = 0

This equation can be solved by using a graphing calculator or factoring method to find the values of x. The solutions will form intervals that represent the values of x that satisfy the inequality, and the union of these intervals will be the solution set.

The solution set will depend on the values of x that satisfy the inequality (x-4)(x + 1)(x-6) - 220 ≥ 0.

Answer 2

In interval notation, the solution to the inequality can be written as:
`(-\infty, -1] \cup [4, +\infty)`.

How to solve inequality.

To solve the inequality (x - 4) ( x + 1) (x - 6)² ≥ 0, we need to set each term in the with their parentheses to zero, and test for their intervals at critical points.

Given that:

(x - 4) ( x + 1) (x - 6)² ≥ 0

x - 4 ≥ 0

x ≥ 4

x + 1 ≥ 0

x ≥ -1

(x - 6)² ≥ 0

(x - 6) ≥ 0

x ≥ 6

Thus, the critical points that represents the interval of the given function is at x ≤ -1 or x ≥ 4. In interval notation, the solution to the inequality can be written as:
`(-\infty, -1] \cup [4, +\infty)`.

The complete question.

Solve the following inequality.

(x - 4) ( x + 1) (x - 6)² ≥ 0

Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".