Question

Solve the following inequality algebraically.
x²-16x +60 ≥ 0

Answer 1

`\sf \large \: x≤6 \: or \: x≥10`

Explanation:

Let's solve your inequality step-by-step.

x2−16x+60≥0

Let's find the critical points of the inequality.

x2−16x+60=0

(x−6)(x−10)=0(Factor left side of equation)

x−6=0 or x−10=0(Set factors equal to 0)

x=6 or x=10

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x≤6(Works in original inequality)

6≤x≤10(Doesn't work in original inequality)

x≥10(Works in original inequality)