Solve (3x 10)(2x^2 1)(2-x)>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x < 2

Alternative Form

x \in (0, 2)

Evaluate

(3 x \times 10) (2 x^{2} \times 1) (2 - x) > 0

Remove the parentheses

3 x \times 10 \times 2 x^{2} \times 1 \times (2 - x) > 0

Multiply the terms

More Steps

60 x^{3} (2 - x) > 0

Rewrite the expression

60 x^{3} (2 - x) = 0

Elimination the left coefficient

x^{3} (2 - x) = 0

Separate the equation into 2 possible cases

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

The only way a power can be 0 is when the base equals 0

x = 0 2 - x = 0

Solve the equation

More Steps

x = 0 x = 2

Determine the test intervals using the critical values

x < 0 0 < x < 2 x > 2

Choose a value form each interval

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

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} = 1 x_{3} = 3

To determine if 0 < x < 2 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 0 < x < 2 is the solution x_{3} = 3

To determine if x > 2 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 2 is the solution x > 2 is not a solution

Solution

0 < x < 2

Alternative Form

x \in (0, 2)

Show Solution