Solve b*b-8-10≥-12

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for b

b \in (- \infty, - 6] \cup [6, + \infty)

Evaluate

b \times b - 8 - 10 \geq - 12

Simplify

More Steps

b^{2} - 18 \geq - 12

Move the expression to the left side

b^{2} - 18 - (- 12) \geq 0

Subtract the numbers

More Steps

b^{2} - 6 \geq 0

Rewrite the expression

b^{2} - 6 = 0

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

b^{2} = 0 + 6

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

b^{2} = 6

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

b = \pm 6

Separate the equation into 2 possible cases

b = 6 b = - 6

Determine the test intervals using the critical values

b < - 6 - 6 < b < 6 b > 6

Choose a value form each interval

b_{1} = - 3 b_{2} = 0 b_{3} = 3

To determine if b < - 6 is the solution to the inequality,test if the chosen value b = - 3 satisfies the initial inequality

More Steps

b < - 6 is the solution b_{2} = 0 b_{3} = 3

To determine if - 6 < b < 6 is the solution to the inequality,test if the chosen value b = 0 satisfies the initial inequality

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b < - 6 is the solution - 6 < b < 6 is not a solution b_{3} = 3

To determine if b > 6 is the solution to the inequality,test if the chosen value b = 3 satisfies the initial inequality

More Steps

b < - 6 is the solution - 6 < b < 6 is not a solution b > 6 is the solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

b \leq - 6 is the solution b \geq 6 is the solution

Solution

b \in (- \infty, - 6] \cup [6, + \infty)

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