Solve y 1 > 4y^4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < y < \frac{3 2}{2}

Alternative Form

y \in (0, \frac{3 2}{2})

Evaluate

y \times 1 > 4 y^{4}

Any expression multiplied by 1 remains the same

y > 4 y^{4}

Move the expression to the left side

y - 4 y^{4} > 0

Rewrite the expression

y - 4 y^{4} = 0

Factor the expression

y (1 - 4 y^{3}) = 0

Separate the equation into 2 possible cases

y = 0 1 - 4 y^{3} = 0

Solve the equation

More Steps

y = 0 y = \frac{3 2}{2}

Determine the test intervals using the critical values

y < 0 0 < y < \frac{3 2}{2} y > \frac{3 2}{2}

Choose a value form each interval

y_{1} = - 1 y_{2} = \frac{3 2}{4} y_{3} = 2

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

More Steps

y < 0 is not a solution y_{2} = \frac{3 2}{4} y_{3} = 2

To determine if 0 < y < \frac{3 2}{2} is the solution to the inequality,test if the chosen value y = \frac{3 2}{4} satisfies the initial inequality

More Steps

y < 0 is not a solution 0 < y < \frac{3 2}{2} is the solution y_{3} = 2

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

More Steps

y < 0 is not a solution 0 < y < \frac{3 2}{2} is the solution y > \frac{3 2}{2} is not a solution

Solution

0 < y < \frac{3 2}{2}

Alternative Form

y \in (0, \frac{3 2}{2})

Show Solution