Solve x^2/2 >= 2x^2/3

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x = 0

Evaluate

\frac{x ^{2}}{2} \geq 2 \times \frac{x ^{2}}{3}

Multiply the terms

\frac{x ^{2}}{2} \geq \frac{2 x ^{2}}{3}

Multiply both sides of the inequality by 6

\frac{x ^{2}}{2} \times 6 \geq \frac{2 x ^{2}}{3} \times 6

Multiply the terms

More Steps

3 x^{2} \geq \frac{2 x ^{2}}{3} \times 6

Multiply the terms

More Steps

3 x^{2} \geq 4 x^{2}

Move the expression to the left side

3 x^{2} - 4 x^{2} \geq 0

Subtract the terms

More Steps

- x^{2} \geq 0

Rewrite the expression

- x^{2} = 0

Change the signs on both sides of the equation

x^{2} = 0

The only way a power can be 0 is when the base equals 0

x = 0

Determine the test intervals using the critical values

x < 0 x > 0

Choose a value form each interval

x_{1} = - 1 x_{2} = 1

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x_{2} = 1

To determine if x > 0 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x > 0 is not a solution

Solution

x = 0

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