Solve 2x^2 2x 1 - (15(x -1))/2 > 2x(x 1)

Question

Solve the inequality

x > - 1.528759

Alternative Form

x \in (- 1.528759, + \infty)

Evaluate

2 x^{2} \times 2 x \times 1 - (15 (x - 1)) \div 2 > 2 x (x \times 1)

Remove the parentheses

2 x^{2} \times 2 x \times 1 - (15 (x - 1)) \div 2 > 2 x \times x \times 1

Simplify

More Steps

4 x^{3} - \frac{15 ( x - 1 )}{2} > 2 x \times x \times 1

Multiply the terms

More Steps

4 x^{3} - \frac{15 ( x - 1 )}{2} > 2 x^{2}

Multiply both sides of the inequality by 2

(4 x^{3} - \frac{15 ( x - 1 )}{2}) \times 2 > 2 x^{2} \times 2

Multiply the terms

More Steps

8 x^{3} - 15 (x - 1) > 2 x^{2} \times 2

Multiply the terms

8 x^{3} - 15 (x - 1) > 4 x^{2}

Move the expression to the left side

8 x^{3} - 15 (x - 1) - 4 x^{2} > 0

Expand the expression

More Steps

8 x^{3} - 15 x + 15 - 4 x^{2} > 0

Rewrite the expression

8 x^{3} - 15 x + 15 - 4 x^{2} = 0

Find the critical values by solving the corresponding equation

x \approx - 1.528759

Determine the test intervals using the critical values

x < - 1.528759 x > - 1.528759

Choose a value form each interval

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

To determine if x < - 1.528759 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 1.528759 is not a solution x_{2} = - 1

To determine if x > - 1.528759 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - 1.528759 is not a solution x > - 1.528759 is the solution

Solution

x > - 1.528759

Alternative Form

x \in (- 1.528759, + \infty)

Show Solution