Solve 8x^2≥310x

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

x \in (- \infty, 0] \cup [\frac{155}{4}, + \infty)

Evaluate

8 x^{2} \geq 310 x

Move the expression to the left side

8 x^{2} - 310 x \geq 0

Rewrite the expression

8 x^{2} - 310 x = 0

Factor the expression

More Steps

2 x (4 x - 155) = 0

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

2 x = 0 4 x - 155 = 0

Solve the equation for x

x = 0 4 x - 155 = 0

Solve the equation for x

More Steps

x = 0 x = \frac{155}{4}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{155}{4} x > \frac{155}{4}

Choose a value form each interval

x_{1} = - 1 x_{2} = 19 x_{3} = 40

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} = 19 x_{3} = 40

To determine if 0 < x < \frac{155}{4} is the solution to the inequality,test if the chosen value x = 19 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{155}{4} is not a solution x_{3} = 40

To determine if x > \frac{155}{4} is the solution to the inequality,test if the chosen value x = 40 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{155}{4} is not a solution x > \frac{155}{4} is the solution

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

x \leq 0 is the solution x \geq \frac{155}{4} is the solution

Solution

x \in (- \infty, 0] \cup [\frac{155}{4}, + \infty)

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