Question

Solve the inequality. Write the solution in interval notation.
(x+14)/(x-8)≥ 1

Answer 1

if x-8> 0 , then
x+14 ≥ x-8
14 ≥ -8 , so true for all x's

if x-8 < 0
x+14 ≤ x-8
14 ≤ -8 , no way!

so true for x > 8

check:
take a value > 8
e.g. x = 10
statement becomes
24/2 ≥ 1 , true

take a value < 8
e.g
x = 1
statement becomes
15/-7≥1 , false
how about x = -20
statement becomes
-6/-28 ≥ 1 or 3/14 ≥ 1 false

solution x > 8