Solve 7x - x^2 > 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 < 7

Alternative Form

x \in (0, 7)

Evaluate

7 x - x^{2} > 0

Rewrite the expression

7 x - x^{2} = 0

Factor the expression

More Steps

x (7 - x) = 0

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

x = 0 7 - x = 0

Solve the equation for x

More Steps

x = 0 x = 7

Determine the test intervals using the critical values

x < 0 0 < x < 7 x > 7

Choose a value form each interval

x_{1} = - 1 x_{2} = 4 x_{3} = 8

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} = 4 x_{3} = 8

To determine if 0 < x < 7 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 7 is the solution x_{3} = 8

To determine if x > 7 is the solution to the inequality,test if the chosen value x = 8 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 7 is the solution x > 7 is not a solution

Solution

0 < x < 7

Alternative Form

x \in (0, 7)

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