Question

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

Answer 1

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.