Solve v^2 < v1 - ScanMath

Evaluate

v^{2} < v \times 1

Any expression multiplied by 1 remains the same

v^{2} < v

Move the expression to the left side

v^{2} - v < 0

Rewrite the expression

v^{2} - v = 0

Factor the expression

More Steps

v (v - 1) = 0

When the product of factors equals 0,at least one factor is 0

v = 0 v - 1 = 0

Solve the equation for v

More Steps

v = 0 v = 1

Determine the test intervals using the critical values

v < 0 0 < v < 1 v > 1

Choose a value form each interval

v_{1} = - 1 v_{2} = \frac{1}{2} v_{3} = 2

To determine if v < 0 is the solution to the inequality,test if the chosen value v = - 1 satisfies the initial inequality

More Steps

v < 0 is not a solution v_{2} = \frac{1}{2} v_{3} = 2

To determine if 0 < v < 1 is the solution to the inequality,test if the chosen value v = \frac{1}{2} satisfies the initial inequality

More Steps

v < 0 is not a solution 0 < v < 1 is the solution v_{3} = 2

To determine if v > 1 is the solution to the inequality,test if the chosen value v = 2 satisfies the initial inequality

More Steps

v < 0 is not a solution 0 < v < 1 is the solution v > 1 is not a solution

Solution

0 < v < 1

Alternative Form

v \in (0, 1)

Solve the inequality