Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for q
−22≤q≤22
Alternative Form
q∈[−22,22]
Evaluate
q2≤8
Move the expression to the left side
q2−8≤0
Rewrite the expression
q2−8=0
Move the constant to the right-hand side and change its sign
q2=0+8
Removing 0 doesn't change the value,so remove it from the expression
q2=8
Take the root of both sides of the equation and remember to use both positive and negative roots
q=±8
Simplify the expression
More Steps
Evaluate
8
Write the expression as a product where the root of one of the factors can be evaluated
4×2
Write the number in exponential form with the base of 2
22×2
The root of a product is equal to the product of the roots of each factor
22×2
Reduce the index of the radical and exponent with 2
22
q=±22
Separate the equation into 2 possible cases
q=22q=−22
Determine the test intervals using the critical values
q<−22−22<q<22q>22
Choose a value form each interval
q1=−4q2=0q3=4
To determine if q<−22 is the solution to the inequality,test if the chosen value q=−4 satisfies the initial inequality
More Steps
Evaluate
(−4)2≤8
Calculate
42≤8
Calculate
16≤8
Check the inequality
false
q<−22 is not a solutionq2=0q3=4
To determine if −22<q<22 is the solution to the inequality,test if the chosen value q=0 satisfies the initial inequality
More Steps
Evaluate
02≤8
Calculate
0≤8
Check the inequality
true
q<−22 is not a solution−22<q<22 is the solutionq3=4
To determine if q>22 is the solution to the inequality,test if the chosen value q=4 satisfies the initial inequality
More Steps
Evaluate
42≤8
Calculate
16≤8
Check the inequality
false
q<−22 is not a solution−22<q<22 is the solutionq>22 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−22≤q≤22 is the solution
Solution
−22≤q≤22
Alternative Form
q∈[−22,22]
Show Solution
