Solve x^34>50 - Socratic AI (ScanMath)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x > \frac{3 100}{2}

Alternative Form

x \in (\frac{3 100}{2}, + \infty)

Evaluate

x^{3} \times 4 > 50

Use the commutative property to reorder the terms

4 x^{3} > 50

Move the expression to the left side

4 x^{3} - 50 > 0

Rewrite the expression

4 x^{3} - 50 = 0

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

4 x^{3} = 0 + 50

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

4 x^{3} = 50

Divide both sides

\frac{4 x ^{3}}{4} = \frac{50}{4}

Divide the numbers

x^{3} = \frac{50}{4}

Cancel out the common factor 2

x^{3} = \frac{25}{2}

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

3 x^{3} = 3 \frac{25}{2}

Calculate

x = 3 \frac{25}{2}

Simplify the root

More Steps

x = \frac{3 100}{2}

Determine the test intervals using the critical values

x < \frac{3 100}{2} x > \frac{3 100}{2}

Choose a value form each interval

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

To determine if x < \frac{3 100}{2} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < \frac{3 100}{2} is not a solution x_{2} = 3

To determine if x > \frac{3 100}{2} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < \frac{3 100}{2} is not a solution x > \frac{3 100}{2} is the solution

Solution

x > \frac{3 100}{2}

Alternative Form

x \in (\frac{3 100}{2}, + \infty)

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