Solve 2x^3<5x-6 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x < - 2

Alternative Form

x \in (- \infty, - 2)

Evaluate

2 x^{3} < 5 x - 6

Move the expression to the left side

2 x^{3} - (5 x - 6) < 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 x^{3} - 5 x + 6 < 0

Rewrite the expression

2 x^{3} - 5 x + 6 = 0

Factor the expression

(x + 2) (2 x^{2} - 4 x + 3) = 0

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

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

Solve the equation

More Steps

x = - 2 x \in / R

Find the union

x = - 2

Determine the test intervals using the critical values

x < - 2 x > - 2

Choose a value form each interval

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

To determine if x < - 2 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 2 is the solution x_{2} = - 1

To determine if x > - 2 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - 2 is the solution x > - 2 is not a solution

Solution

x < - 2

Alternative Form

x \in (- \infty, - 2)

Show Solution