Solve 9<d^32 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for d

d > \frac{3 36}{2}

Alternative Form

d \in (\frac{3 36}{2}, + \infty)

Evaluate

9 < d^{3} \times 2

Use the commutative property to reorder the terms

9 < 2 d^{3}

Move the expression to the left side

9 - 2 d^{3} < 0

Rewrite the expression

9 - 2 d^{3} = 0

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

- 2 d^{3} = 0 - 9

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

- 2 d^{3} = - 9

Change the signs on both sides of the equation

2 d^{3} = 9

Divide both sides

\frac{2 d ^{3}}{2} = \frac{9}{2}

Divide the numbers

d^{3} = \frac{9}{2}

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

3 d^{3} = 3 \frac{9}{2}

Calculate

d = 3 \frac{9}{2}

Simplify the root

More Steps

d = \frac{3 36}{2}

Determine the test intervals using the critical values

d < \frac{3 36}{2} d > \frac{3 36}{2}

Choose a value form each interval

d_{1} = 1 d_{2} = 3

To determine if d < \frac{3 36}{2} is the solution to the inequality,test if the chosen value d = 1 satisfies the initial inequality

More Steps

d < \frac{3 36}{2} is not a solution d_{2} = 3

To determine if d > \frac{3 36}{2} is the solution to the inequality,test if the chosen value d = 3 satisfies the initial inequality

More Steps

d < \frac{3 36}{2} is not a solution d > \frac{3 36}{2} is the solution

Solution

d > \frac{3 36}{2}

Alternative Form

d \in (\frac{3 36}{2}, + \infty)

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