2х2-7х+6<0

To solve the inequality 2x^2 - 7x + 6 < 0, we need to find the values of x that satisfy the inequality.

First, let's factor the quadratic expression:

2x^2 - 7x + 6 = (2x - 3)(x - 2)

Now, we can determine the critical points by setting each factor equal to zero:

2x - 3 = 0 x = 3/2

x - 2 = 0 x = 2

The critical points are x = 3/2 and x = 2.

Next, we can create a number line and test intervals to determine the sign of the expression:

Choose a value less than 3/2, such as x = 1: 2(1)^2 - 7(1) + 6 = 1 < 0

Choose a value between 3/2 and 2, such as x = 3/2 + 1/4 = 7/4: 2(7/4)^2 - 7(7/4) + 6 = 7/8 > 0

Choose a value greater than 2, such as x = 3: 2(3)^2 - 7(3) + 6 = -3 < 0

Based on these tests, we can conclude that the expression is positive between x = 3/2 and x = 2, and negative elsewhere.

Therefore, the solution to the inequality 2x^2 - 7x + 6 < 0 is 3/2 < x < 2.