Solve 77<5x^33 - Socratic AI (ScanMath)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x > \frac{3 17325}{15}

Alternative Form

x \in (\frac{3 17325}{15}, + \infty)

Evaluate

77 < 5 x^{3} \times 3

Multiply the terms

77 < 15 x^{3}

Move the expression to the left side

77 - 15 x^{3} < 0

Rewrite the expression

77 - 15 x^{3} = 0

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

- 15 x^{3} = 0 - 77

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

- 15 x^{3} = - 77

Change the signs on both sides of the equation

15 x^{3} = 77

Divide both sides

\frac{15 x ^{3}}{15} = \frac{77}{15}

Divide the numbers

x^{3} = \frac{77}{15}

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

3 x^{3} = 3 \frac{77}{15}

Calculate

x = 3 \frac{77}{15}

Simplify the root

More Steps

x = \frac{3 17325}{15}

Determine the test intervals using the critical values

x < \frac{3 17325}{15} x > \frac{3 17325}{15}

Choose a value form each interval

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

To determine if x < \frac{3 17325}{15} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < \frac{3 17325}{15} is not a solution x_{2} = 3

To determine if x > \frac{3 17325}{15} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < \frac{3 17325}{15} is not a solution x > \frac{3 17325}{15} is the solution

Solution

x > \frac{3 17325}{15}

Alternative Form

x \in (\frac{3 17325}{15}, + \infty)

Show Solution