Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
0<y<232
Alternative Form
y∈(0,232)
Evaluate
y×1>4y4
Any expression multiplied by 1 remains the same
y>4y4
Move the expression to the left side
y−4y4>0
Rewrite the expression
y−4y4=0
Factor the expression
y(1−4y3)=0
Separate the equation into 2 possible cases
y=01−4y3=0
Solve the equation
More Steps

Evaluate
1−4y3=0
Move the constant to the right-hand side and change its sign
−4y3=0−1
Removing 0 doesn't change the value,so remove it from the expression
−4y3=−1
Change the signs on both sides of the equation
4y3=1
Divide both sides
44y3=41
Divide the numbers
y3=41
Take the 3-th root on both sides of the equation
3y3=341
Calculate
y=341
Simplify the root
More Steps

Evaluate
341
To take a root of a fraction,take the root of the numerator and denominator separately
3431
Simplify the radical expression
341
Multiply by the Conjugate
34×342342
Simplify
34×342232
Multiply the numbers
22232
Reduce the fraction
232
y=232
y=0y=232
Determine the test intervals using the critical values
y<00<y<232y>232
Choose a value form each interval
y1=−1y2=432y3=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

Evaluate
−1>4(−1)4
Simplify
More Steps

Evaluate
4(−1)4
Evaluate the power
4×1
Any expression multiplied by 1 remains the same
4
−1>4
Check the inequality
false
y<0 is not a solutiony2=432y3=2
To determine if 0<y<232 is the solution to the inequality,test if the chosen value y=432 satisfies the initial inequality
More Steps

Evaluate
432>4(432)4
Multiply the terms
More Steps

Evaluate
4(432)4
Evaluate the power
4×12832
Multiply the numbers
3232
432>3232
Calculate
0.31498>3232
Calculate
0.31498>0.039373
Check the inequality
true
y<0 is not a solution0<y<232 is the solutiony3=2
To determine if y>232 is the solution to the inequality,test if the chosen value y=2 satisfies the initial inequality
More Steps

Evaluate
2>4×24
Multiply the terms
More Steps

Evaluate
4×24
Rewrite the expression
22×24
Rewrite the expression
22+4
Calculate
26
2>26
Calculate
2>64
Check the inequality
false
y<0 is not a solution0<y<232 is the solutiony>232 is not a solution
Solution
0<y<232
Alternative Form
y∈(0,232)
Show Solution
