Question
Solve the inequality
x∈∅
Alternative Form
No solution
Evaluate
2x1<−3x4<5x10
Separate into two inequalities
{2x×1<−3x4−3x4<5x×10
Solve the inequality
More Steps

Evaluate
2x×1<−3x4
Multiply the terms
2x<−3x4
Add or subtract both sides
2x−(−3x4)<0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2x+3x4<0
Factor the expression
x(2+3x3)<0
Separate the inequality into 2 possible cases
{x>02+3x3<0{x<02+3x3>0
Solve the inequality
More Steps

Evaluate
2+3x3<0
Rewrite the expression
3x3<−2
Divide both sides
33x3<3−2
Divide the numbers
x3<3−2
Use b−a=−ba=−ba to rewrite the fraction
x3<−32
Take the 3-th root on both sides of the equation
3x3<3−32
Calculate
x<3−32
Simplify the root
x<−3318
{x>0x<−3318{x<02+3x3>0
Solve the inequality
More Steps

Evaluate
2+3x3>0
Rewrite the expression
3x3>−2
Divide both sides
33x3>3−2
Divide the numbers
x3>3−2
Use b−a=−ba=−ba to rewrite the fraction
x3>−32
Take the 3-th root on both sides of the equation
3x3>3−32
Calculate
x>3−32
Simplify the root
x>−3318
{x>0x<−3318{x<0x>−3318
Find the intersection
x∈∅{x<0x>−3318
Find the intersection
x∈∅−3318<x<0
Find the union
−3318<x<0
{−3318<x<0−3x4<5x×10
Solve the inequality
More Steps

Evaluate
−3x4<5x×10
Multiply the terms
−3x4<50x
Add or subtract both sides
−3x4−50x<0
Factor the expression
−x(3x3+50)<0
Divide both sides
x(3x3+50)>0
Separate the inequality into 2 possible cases
{x>03x3+50>0{x<03x3+50<0
Solve the inequality
More Steps

Evaluate
3x3+50>0
Move the constant to the right side
3x3>−50
Divide both sides
33x3>3−50
Divide the numbers
x3>3−50
Use b−a=−ba=−ba to rewrite the fraction
x3>−350
Take the 3-th root on both sides of the equation
3x3>3−350
Calculate
x>3−350
Simplify the root
x>−33450
{x>0x>−33450{x<03x3+50<0
Solve the inequality
More Steps

Evaluate
3x3+50<0
Move the constant to the right side
3x3<−50
Divide both sides
33x3<3−50
Divide the numbers
x3<3−50
Use b−a=−ba=−ba to rewrite the fraction
x3<−350
Take the 3-th root on both sides of the equation
3x3<3−350
Calculate
x<3−350
Simplify the root
x<−33450
{x>0x>−33450{x<0x<−33450
Find the intersection
x>0{x<0x<−33450
Find the intersection
x>0x<−33450
Find the union
x∈(−∞,−33450)∪(0,+∞)
{−3318<x<0x∈(−∞,−33450)∪(0,+∞)
Solution
x∈∅
Alternative Form
No solution
Show Solution
