Solve (3x^5)/2 -4<7

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x < \frac{5 1782}{3}

Alternative Form

x \in (- \infty, \frac{5 1782}{3})

Evaluate

\frac{3 x ^{5}}{2} - 4 < 7

Multiply both sides of the inequality by 2

(\frac{3 x ^{5}}{2} - 4) \times 2 < 7 \times 2

Multiply the terms

More Steps

3 x^{5} - 8 < 7 \times 2

Multiply the terms

3 x^{5} - 8 < 14

Move the expression to the left side

3 x^{5} - 8 - 14 < 0

Subtract the numbers

3 x^{5} - 22 < 0

Rewrite the expression

3 x^{5} - 22 = 0

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

3 x^{5} = 0 + 22

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

3 x^{5} = 22

Divide both sides

\frac{3 x ^{5}}{3} = \frac{22}{3}

Divide the numbers

x^{5} = \frac{22}{3}

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

5 x^{5} = 5 \frac{22}{3}

Calculate

x = 5 \frac{22}{3}

Simplify the root

More Steps

x = \frac{5 1782}{3}

Determine the test intervals using the critical values

x < \frac{5 1782}{3} x > \frac{5 1782}{3}

Choose a value form each interval

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

To determine if x < \frac{5 1782}{3} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < \frac{5 1782}{3} is the solution x_{2} = 2

To determine if x > \frac{5 1782}{3} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{5 1782}{3} is the solution x > \frac{5 1782}{3} is not a solution

Solution

x < \frac{5 1782}{3}

Alternative Form

x \in (- \infty, \frac{5 1782}{3})

Show Solution