Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for z
z∈(−∞,−2]∪[2,+∞)
Evaluate
2≤z2
Move the expression to the left side
2−z2≤0
Rewrite the expression
2−z2=0
Move the constant to the right-hand side and change its sign
−z2=0−2
Removing 0 doesn't change the value,so remove it from the expression
−z2=−2
Change the signs on both sides of the equation
z2=2
Take the root of both sides of the equation and remember to use both positive and negative roots
z=±2
Separate the equation into 2 possible cases
z=2z=−2
Determine the test intervals using the critical values
z<−2−2<z<2z>2
Choose a value form each interval
z1=−2z2=0z3=2
To determine if z<−2 is the solution to the inequality,test if the chosen value z=−2 satisfies the initial inequality
More Steps
Evaluate
2≤(−2)2
Calculate
2≤22
Calculate
2≤4
Check the inequality
true
z<−2 is the solutionz2=0z3=2
To determine if −2<z<2 is the solution to the inequality,test if the chosen value z=0 satisfies the initial inequality
More Steps
Evaluate
2≤02
Calculate
2≤0
Check the inequality
false
z<−2 is the solution−2<z<2 is not a solutionz3=2
To determine if z>2 is the solution to the inequality,test if the chosen value z=2 satisfies the initial inequality
More Steps
Evaluate
2≤22
Calculate
2≤4
Check the inequality
true
z<−2 is the solution−2<z<2 is not a solutionz>2 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
z≤−2 is the solutionz≥2 is the solution
Solution
z∈(−∞,−2]∪[2,+∞)
Show Solution
