Solve (6x-5)/(4x 1) < 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x < \frac{5}{6}

Alternative Form

x \in (0, \frac{5}{6})

Evaluate

\frac{6 x - 5}{4 x \times 1} < 0

Find the domain

More Steps

\frac{6 x - 5}{4 x \times 1} < 0, x \neq = 0

Multiply the terms

\frac{6 x - 5}{4 x} < 0

Set the numerator and denominator of \frac{6 x - 5}{4 x} equal to 0 to find the values of x where sign changes may occur

6 x - 5 = 0 4 x = 0

Calculate

More Steps

x = \frac{5}{6} 4 x = 0

Calculate

x = \frac{5}{6} x = 0

Determine the test intervals using the critical values

x < 0 0 < x < \frac{5}{6} x > \frac{5}{6}

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{5}{12} x_{3} = 2

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x_{2} = \frac{5}{12} x_{3} = 2

To determine if 0 < x < \frac{5}{6} is the solution to the inequality,test if the chosen value x = \frac{5}{12} satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{5}{6} is the solution x_{3} = 2

To determine if x > \frac{5}{6} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{5}{6} is the solution x > \frac{5}{6} is not a solution

The original inequality is a strict inequality,so does not include the critical value ,the final solution is 0 < x < \frac{5}{6}

0 < x < \frac{5}{6}

Check if the solution is in the defined range

0 < x < \frac{5}{6}, x \neq = 0

Solution

0 < x < \frac{5}{6}

Alternative Form

x \in (0, \frac{5}{6})

Show Solution