Solve -8(x-3) 6(13x)<-2x 7x

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{936}{305}, + \infty)

Evaluate

- 8 (x - 3) \times 6 \times 13 x < - 2 x \times 7 x

Multiply

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- 624 x (x - 3) < - 2 x \times 7 x

Multiply

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- 624 x (x - 3) < - 14 x^{2}

Move the expression to the left side

- 624 x (x - 3) - (- 14 x^{2}) < 0

Subtract the terms

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- 610 x^{2} + 1872 x < 0

Rewrite the expression

- 610 x^{2} + 1872 x = 0

Factor the expression

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- 2 x (305 x - 936) = 0

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

- 2 x = 0 305 x - 936 = 0

Solve the equation for x

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x = 0 305 x - 936 = 0

Solve the equation for x

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x = 0 x = \frac{936}{305}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{936}{305} x > \frac{936}{305}

Choose a value form each interval

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

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

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x < 0 is the solution x_{2} = 2 x_{3} = 4

To determine if 0 < x < \frac{936}{305} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

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x < 0 is the solution 0 < x < \frac{936}{305} is not a solution x_{3} = 4

To determine if x > \frac{936}{305} is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

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x < 0 is the solution 0 < x < \frac{936}{305} is not a solution x > \frac{936}{305} is the solution

Solution

x \in (- \infty, 0) \cup (\frac{936}{305}, + \infty)

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