Solve v* v-12 >4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for v

v \in (- \infty, - 4) \cup (4, + \infty)

Evaluate

v \times v - 12 > 4

Multiply the terms

v^{2} - 12 > 4

Move the expression to the left side

v^{2} - 12 - 4 > 0

Subtract the numbers

v^{2} - 16 > 0

Rewrite the expression

v^{2} - 16 = 0

Move the constant to the right-hand side and change its sign

v^{2} = 0 + 16

Removing 0 doesn't change the value,so remove it from the expression

v^{2} = 16

Take the root of both sides of the equation and remember to use both positive and negative roots

v = \pm 16

Simplify the expression

More Steps

v = \pm 4

Separate the equation into 2 possible cases

v = 4 v = - 4

Determine the test intervals using the critical values

v < - 4 - 4 < v < 4 v > 4

Choose a value form each interval

v_{1} = - 5 v_{2} = 0 v_{3} = 5

To determine if v < - 4 is the solution to the inequality,test if the chosen value v = - 5 satisfies the initial inequality

More Steps

v < - 4 is the solution v_{2} = 0 v_{3} = 5

To determine if - 4 < v < 4 is the solution to the inequality,test if the chosen value v = 0 satisfies the initial inequality

More Steps

v < - 4 is the solution - 4 < v < 4 is not a solution v_{3} = 5

To determine if v > 4 is the solution to the inequality,test if the chosen value v = 5 satisfies the initial inequality

More Steps

v < - 4 is the solution - 4 < v < 4 is not a solution v > 4 is the solution

Solution

v \in (- \infty, - 4) \cup (4, + \infty)

Show Solution