Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for b
b∈(−∞,−83)∪(83,+∞)
Evaluate
b×b−43>40
Multiply the terms
b2−43>40
Move the expression to the left side
b2−43−40>0
Subtract the numbers
b2−83>0
Rewrite the expression
b2−83=0
Move the constant to the right-hand side and change its sign
b2=0+83
Removing 0 doesn't change the value,so remove it from the expression
b2=83
Take the root of both sides of the equation and remember to use both positive and negative roots
b=±83
Separate the equation into 2 possible cases
b=83b=−83
Determine the test intervals using the critical values
b<−83−83<b<83b>83
Choose a value form each interval
b1=−10b2=0b3=10
To determine if b<−83 is the solution to the inequality,test if the chosen value b=−10 satisfies the initial inequality
More Steps
Evaluate
(−10)2−43>40
Subtract the numbers
More Steps
Evaluate
(−10)2−43
Simplify
102−43
Evaluate the power
100−43
Subtract the numbers
57
57>40
Check the inequality
true
b<−83 is the solutionb2=0b3=10
To determine if −83<b<83 is the solution to the inequality,test if the chosen value b=0 satisfies the initial inequality
More Steps
Evaluate
02−43>40
Simplify
More Steps
Evaluate
02−43
Calculate
0−43
Removing 0 doesn't change the value,so remove it from the expression
−43
−43>40
Check the inequality
false
b<−83 is the solution−83<b<83 is not a solutionb3=10
To determine if b>83 is the solution to the inequality,test if the chosen value b=10 satisfies the initial inequality
More Steps
Evaluate
102−43>40
Subtract the numbers
More Steps
Evaluate
102−43
Evaluate the power
100−43
Subtract the numbers
57
57>40
Check the inequality
true
b<−83 is the solution−83<b<83 is not a solutionb>83 is the solution
Solution
b∈(−∞,−83)∪(83,+∞)
Show Solution
