Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
−1<v<0
Alternative Form
v∈(−1,0)
Evaluate
v2>v3>v1
Separate into two inequalities
{v2>v3v3>v×1
Solve the inequality
More Steps
Evaluate
v2>v3
Move the expression to the left side
v2−v3>0
Factor the expression
v2(1−v)>0
Separate the inequality into 2 possible cases
{v2>01−v>0{v2<01−v<0
Solve the inequality
More Steps
Evaluate
v2>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 v,except when v2=0
v2=0
The only way a power can be 0 is when the base equals 0
v=0
Exclude the impossible values of v
v=0
{v=01−v>0{v2<01−v<0
Solve the inequality
More Steps
Evaluate
1−v>0
Move the constant to the right side
−v>0−1
Removing 0 doesn't change the value,so remove it from the expression
−v>−1
Change the signs on both sides of the inequality and flip the inequality sign
v<1
{v=0v<1{v2<01−v<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 v
{v=0v<1{v∈/R1−v<0
Solve the inequality
More Steps
Evaluate
1−v<0
Move the constant to the right side
−v<0−1
Removing 0 doesn't change the value,so remove it from the expression
−v<−1
Change the signs on both sides of the inequality and flip the inequality sign
v>1
{v=0v<1{v∈/Rv>1
Find the intersection
v∈(−∞,0)∪(0,1){v∈/Rv>1
Find the intersection
v∈(−∞,0)∪(0,1)v∈/R
Find the union
v∈(−∞,0)∪(0,1)
{v∈(−∞,0)∪(0,1)v3>v×1
Solve the inequality
More Steps
Evaluate
v3>v×1
Any expression multiplied by 1 remains the same
v3>v
Move the expression to the left side
v3−v>0
Factor the expression
v(v2−1)>0
Separate the inequality into 2 possible cases
{v>0v2−1>0{v<0v2−1<0
Solve the inequality
More Steps
Evaluate
v2−1>0
Move the constant to the right side
v2>1
Take the 2-th root on both sides of the inequality
v2>1
Calculate
∣v∣>1
Separate the inequality into 2 possible cases
v>1v<−1
Find the union
v∈(−∞,−1)∪(1,+∞)
{v>0v∈(−∞,−1)∪(1,+∞){v<0v2−1<0
Solve the inequality
More Steps
Evaluate
v2−1<0
Move the constant to the right side
v2<1
Take the 2-th root on both sides of the inequality
v2<1
Calculate
∣v∣<1
Separate the inequality into 2 possible cases
{v<1v>−1
Find the intersection
−1<v<1
{v>0v∈(−∞,−1)∪(1,+∞){v<0−1<v<1
Find the intersection
v>1{v<0−1<v<1
Find the intersection
v>1−1<v<0
Find the union
v∈(−1,0)∪(1,+∞)
{v∈(−∞,0)∪(0,1)v∈(−1,0)∪(1,+∞)
Solution
−1<v<0
Alternative Form
v∈(−1,0)
Show Solution
