Solve 2x^3 < 7 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x < \frac{3 28}{2}

Alternative Form

x \in (- \infty, \frac{3 28}{2})

Evaluate

2 x^{3} < 7

Move the expression to the left side

2 x^{3} - 7 < 0

Rewrite the expression

2 x^{3} - 7 = 0

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

2 x^{3} = 0 + 7

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

2 x^{3} = 7

Divide both sides

\frac{2 x ^{3}}{2} = \frac{7}{2}

Divide the numbers

x^{3} = \frac{7}{2}

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

3 x^{3} = 3 \frac{7}{2}

Calculate

x = 3 \frac{7}{2}

Simplify the root

More Steps

x = \frac{3 28}{2}

Determine the test intervals using the critical values

x < \frac{3 28}{2} x > \frac{3 28}{2}

Choose a value form each interval

x_{1} = 1 x_{2} = 3

To determine if x < \frac{3 28}{2} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < \frac{3 28}{2} is the solution x_{2} = 3

To determine if x > \frac{3 28}{2} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < \frac{3 28}{2} is the solution x > \frac{3 28}{2} is not a solution

Solution

x < \frac{3 28}{2}

Alternative Form

x \in (- \infty, \frac{3 28}{2})

Show Solution