Solve the Inequality 2x^2 - 3x + 1 < 0 on a Number...

We are tasked with solving the quadratic inequality:

\[
2x^2 - 3x + 1 < 0
\]

### Step 1: Solve the corresponding quadratic equation
First, let's solve the quadratic equation \(2x^2 - 3x + 1 = 0\) to find the boundary points where the expression is equal to 0. 

We can use the quadratic formula, which is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \(2x^2 - 3x + 1 = 0\), we have:

- \(a = 2\)
- \(b = -3\)
- \(c = 1\)

Now, applying these values to the quadratic formula:

\[
x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(1)}}{2(2)}
\]

\[
x = \frac{3 \pm \sqrt{9 - 8}}{4}
\]

\[
x = \frac{3 \pm \sqrt{1}}{4}
\]

\[
x = \frac{3 \pm 1}{4}
\]

So, the solutions are:

\[
x_1 = \frac{3 + 1}{4} = 1 \quad \text{and} \quad x_2 = \frac{

Explore how to solve the quadratic inequality 2x^2 - 3x + 1 < 0 with a step-by-step breakdown using the quadratic formula. This algebra problem demonstrates key concepts in solving inequalities and quadratic equations. Suitable for students in Grades 9-11.

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