Question
Evaluate
⎩⎨⎧x>03a−4x2<02x2−b<0⎩⎨⎧x<03a−4x2>02x2−b>0(a,b,x)∈∅
Evaluate
{3xa<4x34x3<2xb
Solve the inequality
More Steps

Evaluate
3xa<4x3
Move the expression to the left side
3xa−4x3<0
Factor the expression
x(3a−4x2)<0
Separate the inequality into 2 possible cases
{x>03a−4x2<0{x<03a−4x2>0
Find the intersection
{3a−4x2<0x>0{x<03a−4x2>0
Find the intersection
{3a−4x2<0x>0{3a−4x2>0x<0
⎩⎨⎧{3a−4x2<0x>0{3a−4x2>0x<04x3<2xb
Rewrite the expression
⎩⎨⎧4x3<2xb3a−4x2<0x>0⎩⎨⎧4x3<2xb3a−4x2>0x<0
Calculate
More Steps

Evaluate
4x3<2xb
Move the expression to the left side
4x3−2xb<0
Factor the expression
2x(2x2−b)<0
Divide both sides
x(2x2−b)<0
Separate the inequality into 2 possible cases
{x>02x2−b<0{x<02x2−b>0
Find the intersection
{2x2−b<0x>0{x<02x2−b>0
Find the intersection
{2x2−b<0x>0{2x2−b>0x<0
⎩⎨⎧{2x2−b<0x>0{2x2−b>0x<03a−4x2<0x>0⎩⎨⎧4x3<2xb3a−4x2>0x<0
Rewrite the expression
⎩⎨⎧3a−4x2<0x>02x2−b<0x>0⎩⎨⎧3a−4x2<0x>02x2−b>0x<0⎩⎨⎧4x3<2xb3a−4x2>0x<0
Calculate
More Steps

Evaluate
⎩⎨⎧3a−4x2<0x>02x2−b<0x>0
Simplify
⎩⎨⎧3a−4x2<0x>02x2−b<0
Find the intersection
⎩⎨⎧x>03a−4x2<02x2−b<0
Find the intersection
⎩⎨⎧3a−4x2<02x2−b<0x>0⎩⎨⎧3a−4x2<0x>02x2−b>0x<0⎩⎨⎧4x3<2xb3a−4x2>0x<0
Calculate
⎩⎨⎧3a−4x2<02x2−b<0x>0
⎩⎨⎧3a−4x2<02x2−b<0x>0⎩⎨⎧3a−4x2<0x>02x2−b>0x<0⎩⎨⎧4x3<2xb3a−4x2>0x<0
Calculate
⎩⎨⎧3a−4x2<02x2−b<0x>0(a,b,x)∈∅⎩⎨⎧4x3<2xb3a−4x2>0x<0
Calculate
More Steps

Evaluate
4x3<2xb
Move the expression to the left side
4x3−2xb<0
Factor the expression
2x(2x2−b)<0
Divide both sides
x(2x2−b)<0
Separate the inequality into 2 possible cases
{x>02x2−b<0{x<02x2−b>0
Find the intersection
{2x2−b<0x>0{x<02x2−b>0
Find the intersection
{2x2−b<0x>0{2x2−b>0x<0
⎩⎨⎧3a−4x2<02x2−b<0x>0(a,b,x)∈∅⎩⎨⎧{2x2−b<0x>0{2x2−b>0x<03a−4x2>0x<0
Rewrite the expression
⎩⎨⎧3a−4x2<02x2−b<0x>0(a,b,x)∈∅⎩⎨⎧3a−4x2>0x<02x2−b<0x>0⎩⎨⎧3a−4x2>0x<02x2−b>0x<0
Calculate
⎩⎨⎧3a−4x2<02x2−b<0x>0(a,b,x)∈∅(a,b,x)∈∅⎩⎨⎧3a−4x2>0x<02x2−b>0x<0
Calculate
More Steps

Evaluate
⎩⎨⎧3a−4x2>0x<02x2−b>0x<0
Simplify
⎩⎨⎧3a−4x2>0x<02x2−b>0
Find the intersection
⎩⎨⎧x<03a−4x2>02x2−b>0
Find the intersection
⎩⎨⎧3a−4x2<02x2−b<0x>0(a,b,x)∈∅(a,b,x)∈∅⎩⎨⎧3a−4x2>02x2−b>0x<0
Calculate
⎩⎨⎧3a−4x2>02x2−b>0x<0
⎩⎨⎧3a−4x2<02x2−b<0x>0(a,b,x)∈∅(a,b,x)∈∅⎩⎨⎧3a−4x2>02x2−b>0x<0
Calculate
⎩⎨⎧x>03a−4x2<02x2−b<0(a,b,x)∈∅(a,b,x)∈∅⎩⎨⎧3a−4x2>02x2−b>0x<0
Calculate
⎩⎨⎧x>03a−4x2<02x2−b<0(a,b,x)∈∅(a,b,x)∈∅⎩⎨⎧x<03a−4x2>02x2−b>0
Solution
⎩⎨⎧x>03a−4x2<02x2−b<0⎩⎨⎧x<03a−4x2>02x2−b>0(a,b,x)∈∅
Show Solution
