Solve the inequality

2r^2-13x+15<0

Step-by-step explanation:

First, factor the inequality and solve for x to find the zeros.

Then, choose test points on the outside of those values and between them.

Plug them in to determine which one(s) yield a negative (< 0).

2x² - 13x + 15 < 0

(2x - 3)(x - 5) < 0

2x - 3 = 0     and      x - 5 = 0

      x = 3/2     and        x = 5

I choose the left test point of 0            (2(0) - 3) × (0 - 5) > 0  (+)

I choose the between test point of 2   (2(2) - 3) × (2 - 5) < 0  (-)

I choose the right test point of 6          (2(6) - 3) × (6 - 5) > 0  (+)

Illustration of Graph:

     +                               ---                                  +

←----|----------o----------------|---------------o--------------|----→

     0          3/2                2                5              6

Since the "between" test point is the only one that yielded a negative, then the solution is the values between 3/2 and 5.

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