Question
Evaluate
⎩⎨⎧y>0x−y>01−x3y>0x3y−1>0⎩⎨⎧y<0x−y>01−x3y<0x3y−1<0(x,y)∈∅
Evaluate
⎩⎨⎧x>y×1y×1>y2x3y2x3>y
Solve the inequality
More Steps

Evaluate
x>y×1
Any expression multiplied by 1 remains the same
x>y
Calculate
x−y>0
⎩⎨⎧x−y>0y×1>y2x3y2x3>y
Solve the inequality
More Steps

Evaluate
y×1>y2x3
Any expression multiplied by 1 remains the same
y>y2x3
Move the expression to the left side
y−y2x3>0
Factor the expression
y(1−x3y)>0
Separate the inequality into 2 possible cases
{y>01−x3y>0{y<01−x3y<0
Find the intersection
{1−x3y>0y>0{y<01−x3y<0
Find the intersection
{1−x3y>0y>0{1−x3y<0y<0
⎩⎨⎧x−y>0{1−x3y>0y>0{1−x3y<0y<0y2x3>y
Rewrite the expression
⎩⎨⎧x−y>0y2x3>y1−x3y>0y>0⎩⎨⎧x−y>0y2x3>y1−x3y<0y<0
Calculate
More Steps

Evaluate
y2x3>y
Move the expression to the left side
y2x3−y>0
Factor the expression
y(x3y−1)>0
Separate the inequality into 2 possible cases
{y>0x3y−1>0{y<0x3y−1<0
Find the intersection
{x3y−1>0y>0{y<0x3y−1<0
Find the intersection
{x3y−1>0y>0{x3y−1<0y<0
⎩⎨⎧x−y>0{x3y−1>0y>0{x3y−1<0y<01−x3y>0y>0⎩⎨⎧x−y>0y2x3>y1−x3y<0y<0
Rewrite the expression
⎩⎨⎧x−y>01−x3y>0y>0x3y−1>0y>0⎩⎨⎧x−y>01−x3y>0y>0x3y−1<0y<0⎩⎨⎧x−y>0y2x3>y1−x3y<0y<0
Calculate
More Steps

Evaluate
⎩⎨⎧x−y>01−x3y>0y>0x3y−1>0y>0
Simplify
⎩⎨⎧x−y>01−x3y>0y>0x3y−1>0
Find the intersection
⎩⎨⎧y>0x−y>01−x3y>0x3y−1>0
Find the intersection
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0⎩⎨⎧x−y>01−x3y>0y>0x3y−1<0y<0⎩⎨⎧x−y>0y2x3>y1−x3y<0y<0
Calculate
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0⎩⎨⎧x−y>01−x3y>0y>0x3y−1<0y<0⎩⎨⎧x−y>0y2x3>y1−x3y<0y<0
Calculate
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0(x,y)∈∅⎩⎨⎧x−y>0y2x3>y1−x3y<0y<0
Calculate
More Steps

Evaluate
y2x3>y
Move the expression to the left side
y2x3−y>0
Factor the expression
y(x3y−1)>0
Separate the inequality into 2 possible cases
{y>0x3y−1>0{y<0x3y−1<0
Find the intersection
{x3y−1>0y>0{y<0x3y−1<0
Find the intersection
{x3y−1>0y>0{x3y−1<0y<0
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0(x,y)∈∅⎩⎨⎧x−y>0{x3y−1>0y>0{x3y−1<0y<01−x3y<0y<0
Rewrite the expression
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0(x,y)∈∅⎩⎨⎧x−y>01−x3y<0y<0x3y−1>0y>0⎩⎨⎧x−y>01−x3y<0y<0x3y−1<0y<0
Calculate
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0(x,y)∈∅(x,y)∈∅⎩⎨⎧x−y>01−x3y<0y<0x3y−1<0y<0
Calculate
More Steps

Evaluate
⎩⎨⎧x−y>01−x3y<0y<0x3y−1<0y<0
Simplify
⎩⎨⎧x−y>01−x3y<0y<0x3y−1<0
Find the intersection
⎩⎨⎧y<0x−y>01−x3y<0x3y−1<0
Find the intersection
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0(x,y)∈∅(x,y)∈∅⎩⎨⎧x−y>01−x3y<0x3y−1<0y<0
Calculate
⎩⎨⎧x−y>01−x3y<0x3y−1<0y<0
⎩⎨⎧x−y>01−x3y>0x3y−1>0y>0(x,y)∈∅(x,y)∈∅⎩⎨⎧x−y>01−x3y<0x3y−1<0y<0
Calculate
⎩⎨⎧y>0x−y>01−x3y>0x3y−1>0(x,y)∈∅(x,y)∈∅⎩⎨⎧x−y>01−x3y<0x3y−1<0y<0
Calculate
⎩⎨⎧y>0x−y>01−x3y>0x3y−1>0(x,y)∈∅(x,y)∈∅⎩⎨⎧y<0x−y>01−x3y<0x3y−1<0
Solution
⎩⎨⎧y>0x−y>01−x3y>0x3y−1>0⎩⎨⎧y<0x−y>01−x3y<0x3y−1<0(x,y)∈∅
Show Solution
