Solve q^39 > 88 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for q

q > \frac{2 3 33}{3}

Alternative Form

q \in (\frac{2 3 33}{3}, + \infty)

Evaluate

q^{3} \times 9 > 88

Use the commutative property to reorder the terms

9 q^{3} > 88

Move the expression to the left side

9 q^{3} - 88 > 0

Rewrite the expression

9 q^{3} - 88 = 0

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

9 q^{3} = 0 + 88

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

9 q^{3} = 88

Divide both sides

\frac{9 q ^{3}}{9} = \frac{88}{9}

Divide the numbers

q^{3} = \frac{88}{9}

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

3 q^{3} = 3 \frac{88}{9}

Calculate

q = 3 \frac{88}{9}

Simplify the root

More Steps

q = \frac{2 3 33}{3}

Determine the test intervals using the critical values

q < \frac{2 3 33}{3} q > \frac{2 3 33}{3}

Choose a value form each interval

q_{1} = 1 q_{2} = 3

To determine if q < \frac{2 3 33}{3} is the solution to the inequality,test if the chosen value q = 1 satisfies the initial inequality

More Steps

q < \frac{2 3 33}{3} is not a solution q_{2} = 3

To determine if q > \frac{2 3 33}{3} is the solution to the inequality,test if the chosen value q = 3 satisfies the initial inequality

More Steps

q < \frac{2 3 33}{3} is not a solution q > \frac{2 3 33}{3} is the solution

Solution

q > \frac{2 3 33}{3}

Alternative Form

q \in (\frac{2 3 33}{3}, + \infty)

Show Solution