Solve (4-2x)⋅(52x)>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

0 < x < 2

Alternative Form

x \in (0, 2)

Evaluate

(4 - 2 x) \times 52 x > 0

Multiply the terms

52 x (4 - 2 x) > 0

Rewrite the expression

52 x (4 - 2 x) = 0

Elimination the left coefficient

x (4 - 2 x) = 0

Separate the equation into 2 possible cases

x = 0 4 - 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)

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