Solve the inequality by separating into cases of 2 x^{2} - 3 x + 1 > 0

x \in \left(-\infty,\frac{1}{2}\right)\cup \left(1,+\infty\right)

\text{Solve for }x of 2 x^{2} - 3 x + 1 > 0

x \in \left(-\infty,\frac{1}{2}\right)\cup \left(1,+\infty\right)

Question :

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

x \in (- \infty, \frac{1}{2}) \cup (1, + \infty)

Evaluate

2 x^{2} - 3 x + 1 > 0

Rewrite the expression

2 x^{2} - 3 x + 1 = 0

Factor the expression

More Steps

(x - 1) (2 x - 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 1 = 0 2 x - 1 = 0

Solve the equation for x

More Steps

x = 1 2 x - 1 = 0

Solve the equation for x

More Steps

x = 1 x = \frac{1}{2}

Determine the test intervals using the critical values

x < \frac{1}{2} \frac{1}{2} < x < 1 x > 1

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{3}{4} x_{3} = 2

To determine if x < \frac{1}{2} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < \frac{1}{2} is the solution x_{2} = \frac{3}{4} x_{3} = 2

To determine if \frac{1}{2} < x < 1 is the solution to the inequality,test if the chosen value x = \frac{3}{4} satisfies the initial inequality

More Steps

x < \frac{1}{2} is the solution \frac{1}{2} < x < 1 is not a solution x_{3} = 2

To determine if x > 1 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{1}{2} is the solution \frac{1}{2} < x < 1 is not a solution x > 1 is the solution

Solution

x \in (- \infty, \frac{1}{2}) \cup (1, + \infty)

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