SOLUTION: Solve the inequality, and express the solution in terms of intervals whenever possible. (Enter your answer using interval notation. If there is no solution, enter NO SOLUTION.) (x

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Question 707026: Solve the inequality, and express the solution in terms of intervals whenever possible. (Enter your answer using interval notation. If there is no solution, enter NO SOLUTION.)
(x + 1)/(2x − 3) > 2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
We do not know if (2x-3) is positive or negative.

Find critical points or point, treating first the equality.

%28x+%2B+1%29%2F%282x+-3%29+%3E+2
Change to "=", and solve to find critical point:
%28%28x%2B1%29%2F%282x-3%29+%29%2A%282x-3%29=2%282x-3%29
x%2B1=2%282x-3%29
x%2B1=4x-6
.
x=7/3, critical point.

2 is less than the critical point, and 3 is greater than the critical point. They are just examples. The values are not too important; just they are on specific intervals of the real line based on the found critical point.

Test using 2, for x<7/3
%282%2B1%29%2F%282%2A2-3%29=3, and 3%3E2, so
x%3C7%2F3 is solution.

Test using 3, for x>7/3
%283%2B1%29%2F%282%2A3-3%29=4%2F3%3E2, FALSE. This means x>7/3 are NOT solutions.

The solution is x%3C7%2F3