Solve 3 < -5x^2x - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x < - \frac{3 75}{5}

Alternative Form

x \in (- \infty, - \frac{3 75}{5})

Evaluate

3 < - 5 x^{2} \times x

Multiply

More Steps

3 < - 5 x^{3}

Move the expression to the left side

3 - (- 5 x^{3}) < 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

3 + 5 x^{3} < 0

Rewrite the expression

3 + 5 x^{3} = 0

Move the constant to the right-hand side and change its sign

5 x^{3} = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

5 x^{3} = - 3

Divide both sides

\frac{5 x ^{3}}{5} = \frac{- 3}{5}

Divide the numbers

x^{3} = \frac{- 3}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{3}{5}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{3}{5}

Calculate

x = 3 - \frac{3}{5}

Simplify the root

More Steps

x = - \frac{3 75}{5}

Determine the test intervals using the critical values

x < - \frac{3 75}{5} x > - \frac{3 75}{5}

Choose a value form each interval

x_{1} = - 2 x_{2} = 0

To determine if x < - \frac{3 75}{5} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{3 75}{5} is the solution x_{2} = 0

To determine if x > - \frac{3 75}{5} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{3 75}{5} is the solution x > - \frac{3 75}{5} is not a solution

Solution

x < - \frac{3 75}{5}

Alternative Form

x \in (- \infty, - \frac{3 75}{5})

Show Solution