Solve the following inequality.
2x^2 <11x+6
Select the correct choice below and, if necessary, fill in the answer box.
A.The solution set is
B.There is no real solution
To solve the inequality 2x^2 < 11x + 6, we first rearrange it into a quadratic inequality set to zero:
2x^2 - 11x - 6 < 0
Next, we can factor this quadratic:
(2x + 1)(x - 6) < 0
Then we can find the critical points by setting each factor equal to zero and solving:
2x + 1 = 0
x = -1/2
x - 6 = 0
x = 6
Now we create a number line with these critical points:
---(-1/2)---(6)---
We test each interval created by the critical points by plugging in a test point. Let's use x = 0 for this purpose:
(2(0) + 1)(0 - 6) < 0
(1)(-6) < 0
-6 < 0
Since this is true, the solution is where the inequality is less than zero, meaning the solution is:
A. The solution set is -1/2 < x < 6.