Answer:
23 --> 27
36 --> one solution; infinitely many solution; no solutions
Explanation:
23: We know that the three angles add up to 180 in a triangle. In this case, 180 = (3x - 9) + (6x) + (45 - x)
180 = 3x + 6z - x - 9 + 45
180 = 8x + 36
144 = 8x
x = 18
m∠C = 45 - x
m∠C = 45 - (18)
m∠C = 27
36: It's just requires some simplifying.
(2x - 3)/3 = -2x/3 - 1/9
3(2x - 3) = -6x - 1 <-- multiplied both sides by 9 to get rid of fractions
6x - 9 = -6x - 1
12x - 9 = -1
12x = 8
x = 2/3 <-- There is only one solution to this equation.
(2x - 3)/3 = 2x/3 - 1
(2x - 3)/3 = 2x/3 - 3/3
(2x - 3)/3 = (2x - 3)/3 <-- Same equation means that the line will overlap each other infinitely, so there are infinitely many solutions. If you simplify it further you will just get 0=0.
(2x - 3)/3 = 2x/3 - 1/9
(2x - 3)/3 = 6x/9 - 1/9
(2x - 3)/3 = (6x - 1)/9
9(2x - 3) = 3(6x - 1) <-- cross multiplication method
18x - 27 = 18x - 3 <-- Same slope but never touching.
-27 = -3 <-- false, so there are no solutions.