Solve 11p^2≤1010p

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for p

0 \leq p \leq \frac{1010}{11}

Alternative Form

p \in [0, \frac{1010}{11}]

Evaluate

11 p^{2} \leq 1010 p

Move the expression to the left side

11 p^{2} - 1010 p \leq 0

Rewrite the expression

11 p^{2} - 1010 p = 0

Factor the expression

More Steps

p (11 p - 1010) = 0

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

p = 0 11 p - 1010 = 0

Solve the equation for p

More Steps

p = 0 p = \frac{1010}{11}

Determine the test intervals using the critical values

p < 0 0 < p < \frac{1010}{11} p > \frac{1010}{11}

Choose a value form each interval

p_{1} = - 1 p_{2} = 46 p_{3} = 93

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

More Steps

p < 0 is not a solution p_{2} = 46 p_{3} = 93

To determine if 0 < p < \frac{1010}{11} is the solution to the inequality,test if the chosen value p = 46 satisfies the initial inequality

More Steps

p < 0 is not a solution 0 < p < \frac{1010}{11} is the solution p_{3} = 93

To determine if p > \frac{1010}{11} is the solution to the inequality,test if the chosen value p = 93 satisfies the initial inequality

More Steps

p < 0 is not a solution 0 < p < \frac{1010}{11} is the solution p > \frac{1010}{11} is not a solution

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

0 \leq p \leq \frac{1010}{11} is the solution

Solution

0 \leq p \leq \frac{1010}{11}

Alternative Form

p \in [0, \frac{1010}{11}]

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