Solve (x-4)/x>=0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, 0) \cup [4, + \infty)

Evaluate

\frac{x - 4}{x} \geq 0

Find the domain

\frac{x - 4}{x} \geq 0, x \neq = 0

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

x - 4 = 0 x = 0

Calculate

More Steps

x = 4 x = 0

Determine the test intervals using the critical values

x < 0 0 < x < 4 x > 4

Choose a value form each interval

x_{1} = - 1 x_{2} = 2 x_{3} = 5

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 the solution x_{2} = 2 x_{3} = 5

To determine if 0 < x < 4 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 4 is not a solution x_{3} = 5

To determine if x > 4 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 4 is not a solution x > 4 is the solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x < 0 is the solution x \geq 4 is the solution

The final solution of the original inequality is x \in (- \infty, 0) \cup [4, + \infty)

x \in (- \infty, 0) \cup [4, + \infty)

Check if the solution is in the defined range

x \in (- \infty, 0) \cup [4, + \infty), x \neq = 0

Solution

x \in (- \infty, 0) \cup [4, + \infty)

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