Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for b
b∈(−∞,−7]∪[7,+∞)
Evaluate
b2≥7
Move the expression to the left side
b2−7≥0
Rewrite the expression
b2−7=0
Move the constant to the right-hand side and change its sign
b2=0+7
Removing 0 doesn't change the value,so remove it from the expression
b2=7
Take the root of both sides of the equation and remember to use both positive and negative roots
b=±7
Separate the equation into 2 possible cases
b=7b=−7
Determine the test intervals using the critical values
b<−7−7<b<7b>7
Choose a value form each interval
b1=−4b2=0b3=4
To determine if b<−7 is the solution to the inequality,test if the chosen value b=−4 satisfies the initial inequality
More Steps
Evaluate
(−4)2≥7
Calculate
42≥7
Calculate
16≥7
Check the inequality
true
b<−7 is the solutionb2=0b3=4
To determine if −7<b<7 is the solution to the inequality,test if the chosen value b=0 satisfies the initial inequality
More Steps
Evaluate
02≥7
Calculate
0≥7
Check the inequality
false
b<−7 is the solution−7<b<7 is not a solutionb3=4
To determine if b>7 is the solution to the inequality,test if the chosen value b=4 satisfies the initial inequality
More Steps
Evaluate
42≥7
Calculate
16≥7
Check the inequality
true
b<−7 is the solution−7<b<7 is not a solutionb>7 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
b≤−7 is the solutionb≥7 is the solution
Solution
b∈(−∞,−7]∪[7,+∞)
Show Solution
