Question

Solve
X + 1/x – 2 ≥ 3

I know you have to subtract the 3 from both sides to get the zero on right of the inequality sign. I don't understand how to make one fraction after I do this.

Answer 1

with brackets,
(x + 1)/(x – 2) ≥ 3
following your idea ...
(x + 1)/(x – 2) - 3 ≥
we need a common denominator of x-2
(x+1 -3x+6)/(x+1) ≥ 0
(-2x+7)(/(x-2) ≥ 0

so I see 2 critical values, x=7,2 and x=2
splitting the number line into 3 sections,
a) less than 7/2
b) between 7/2 and 2
c) greater than 2

pick any arbitrary value in each region, we don't actually have to evaluate it, just worry about the + or -

a) let x = 0 then +/- , does not work
b) let x = 3, then +/+ > 0 , YES
c) let x = 10, then -/+ , no way

so only the numbers between 7/2 and 2 work, but remember x cannot be 2 or else we are dividing by zer.

so the solution is
7/2 ≤ x < 2 , x is a real number

Answer 2

Thank you very much, you have been a great help!!!