Question

Solve the inequality

2r^2-13x+15<0​

Answer 1

x > 2r^2/13 + 15/13

Explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

x > 2r^2/13 + 15/13

Answer 2

Answer:
`\bold{(3)/(2)<x<5\quad \rightarrow \quad \text{Interval Notation}: \bigg((3)/(2),5\bigg)}`

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.