4-x/x-7 >= 0
4-x >= 0 <---- Multiply both sides by x-7
4 >= x <----- add x
4 is an interest point, 7 is also an interest point since you can't let x be seven in the original denominator. everything before 4 is a negative number(so it can't be included in the answer), 4-7 turns into a positive number(which is acceptable), 7 makes the problem blow up, and everything above seven is a positive number.
So the answer is [4,7)
on a number line, that's a dotted 4, bolded line to an open circled 7.
1/(x-3) > 3
1 > 3(x-3) <-------- multiply both sides by x-3
1>3x-9 <--------- distribute the 3
10>3x <------------ add 10
10/3 > x <----- divide by 3
have points on the line, and at 10/3 (little bit greater than three), have an open dot and bolded line to the right
hope I helped!
Edit:
Interval Notation:
(-∞,4]
(10/3,∞)
Second Edit: Screwed up and didn't check
My friend gave me these answers but they both didn't work, now I'm definitely confused.
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