Solve 1> (k^32)/11

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for k

k < \frac{3 44}{2}

Alternative Form

k \in (- \infty, \frac{3 44}{2})

Evaluate

1 > \frac{k ^{3} \times 2}{11}

Use the commutative property to reorder the terms

1 > \frac{2 k ^{3}}{11}

Multiply both sides of the inequality by 11

1 \times 11 > \frac{2 k ^{3}}{11} \times 11

Multiply the terms

11 > \frac{2 k ^{3}}{11} \times 11

Multiply the terms

11 > 2 k^{3}

Move the expression to the left side

11 - 2 k^{3} > 0

Rewrite the expression

11 - 2 k^{3} = 0

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

- 2 k^{3} = 0 - 11

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

- 2 k^{3} = - 11

Change the signs on both sides of the equation

2 k^{3} = 11

Divide both sides

\frac{2 k ^{3}}{2} = \frac{11}{2}

Divide the numbers

k^{3} = \frac{11}{2}

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

3 k^{3} = 3 \frac{11}{2}

Calculate

k = 3 \frac{11}{2}

Simplify the root

More Steps

k = \frac{3 44}{2}

Determine the test intervals using the critical values

k < \frac{3 44}{2} k > \frac{3 44}{2}

Choose a value form each interval

k_{1} = 1 k_{2} = 3

To determine if k < \frac{3 44}{2} is the solution to the inequality,test if the chosen value k = 1 satisfies the initial inequality

More Steps

k < \frac{3 44}{2} is the solution k_{2} = 3

To determine if k > \frac{3 44}{2} is the solution to the inequality,test if the chosen value k = 3 satisfies the initial inequality

More Steps

k < \frac{3 44}{2} is the solution k > \frac{3 44}{2} is not a solution

Solution

k < \frac{3 44}{2}

Alternative Form

k \in (- \infty, \frac{3 44}{2})

Show Solution