Solve 2x^56<74 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x < \frac{5 47952}{6}

Alternative Form

x \in (- \infty, \frac{5 47952}{6})

Evaluate

2 x^{5} \times 6 < 74

Multiply the terms

12 x^{5} < 74

Move the expression to the left side

12 x^{5} - 74 < 0

Rewrite the expression

12 x^{5} - 74 = 0

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

12 x^{5} = 0 + 74

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

12 x^{5} = 74

Divide both sides

\frac{12 x ^{5}}{12} = \frac{74}{12}

Divide the numbers

x^{5} = \frac{74}{12}

Cancel out the common factor 2

x^{5} = \frac{37}{6}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{37}{6}

Calculate

x = 5 \frac{37}{6}

Simplify the root

More Steps

x = \frac{5 47952}{6}

Determine the test intervals using the critical values

x < \frac{5 47952}{6} x > \frac{5 47952}{6}

Choose a value form each interval

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

To determine if x < \frac{5 47952}{6} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < \frac{5 47952}{6} is the solution x_{2} = 2

To determine if x > \frac{5 47952}{6} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{5 47952}{6} is the solution x > \frac{5 47952}{6} is not a solution

Solution

x < \frac{5 47952}{6}

Alternative Form

x \in (- \infty, \frac{5 47952}{6})

Show Solution