Hi I need help. Can you show me how to solve this problem?

Radical Inequalities.
-2 + square root 9-5x greater than or equal to 6

-2 + √(9-5x) ≥ 6

√(9-5x) ≥ 8

since the left side is obviously positive we can square both sides without disturbing the inequality relation
9-5x ≥ 64
-5x ≥ 55
x ≤ -11

testing:
let x = -10
LS = -2 + √59 = 5.68 < 6 , so x = -10 is not good
let x = -12
LS = -2 + √69 = 6.3.. ≥ 6 , so our answer is correct