Question

Solve the inequality:

x+8 over x-1 > OR = 0

Write the solution set in interval notation. Show work/explanation.

Answer 1

Here is how I do these...

First of all it should be obvious that x cannot be 1, or else we are dividing by zero.

I see 2 critical values, namely x = -8 and x = 1
this splits the number line into 3 sections,
1. less than -8
2. between -8 and 1
3. greater than 1

I then pick an "nice" number in each section and mentally check to see if it works in my inequation.
In most cases you don't actually have to work out the answer, just the correct sign of the answer.

1. let x= -10, .... is -/- ≥ 0 ? YES
2. let x = 0, .... is +/- ≥ 0 ? NO
3. let x = +10 ... is +/+ ≥ 0 ? YES

so x ≤ -8 OR x > 1 , x any real number.

You can change that into the "interval notation" that you were taught.

Answer 2

(3x2) (2x4)