Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−23,0)∪(0,23)
Evaluate
(1×x3)>2
Find the domain
(1×x3)>2,x=0
Simplify
More Steps
Evaluate
(1×x3)
Calculate
x3
Rewrite the expression
3×x1
Rewrite the expression
3x1
3x1>2
Calculate
∣x∣3−2∣x∣>0
Separate the inequality into 2 possible cases
{3−2∣x∣>0∣x∣>0{3−2∣x∣<0∣x∣<0
Solve the inequality
More Steps
Evaluate
3−2∣x∣>0
Rewrite the expression
−2∣x∣>−3
Change the signs on both sides of the inequality and flip the inequality sign
2∣x∣<3
Divide both sides
22∣x∣<23
Divide the numbers
∣x∣<23
Separate the inequality into 2 possible cases
{x<23x>−23
Find the intersection
−23<x<23
{−23<x<23∣x∣>0{3−2∣x∣<0∣x∣<0
Solve the inequality
More Steps
Evaluate
∣x∣>0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when ∣x∣=0
∣x∣=0
Evaluate
x=0
Exclude the impossible values of x
x=0
{−23<x<23x=0{3−2∣x∣<0∣x∣<0
Solve the inequality
More Steps
Evaluate
3−2∣x∣<0
Rewrite the expression
−2∣x∣<−3
Change the signs on both sides of the inequality and flip the inequality sign
2∣x∣>3
Divide both sides
22∣x∣>23
Divide the numbers
∣x∣>23
Separate the inequality into 2 possible cases
x>23x<−23
Find the union
x∈(−∞,−23)∪(23,+∞)
{−23<x<23x=0{x∈(−∞,−23)∪(23,+∞)∣x∣<0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is false for any value of x
{−23<x<23x=0{x∈(−∞,−23)∪(23,+∞)x∈/R
Find the intersection
x∈(−23,0)∪(0,23){x∈(−∞,−23)∪(23,+∞)x∈/R
Find the intersection
x∈(−23,0)∪(0,23)x∈/R
Find the union
x∈(−23,0)∪(0,23)
Check if the solution is in the defined range
x∈(−23,0)∪(0,23),x=0
Solution
x∈(−23,0)∪(0,23)
Show Solution
