Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,−5]∪[5,+∞)
Evaluate
x2≥5
Move the expression to the left side
x2−5≥0
Rewrite the expression
x2−5=0
Move the constant to the right-hand side and change its sign
x2=0+5
Removing 0 doesn't change the value,so remove it from the expression
x2=5
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±5
Separate the equation into 2 possible cases
x=5x=−5
Determine the test intervals using the critical values
x<−5−5<x<5x>5
Choose a value form each interval
x1=−3x2=0x3=3
To determine if x<−5 is the solution to the inequality,test if the chosen value x=−3 satisfies the initial inequality
More Steps

Evaluate
(−3)2≥5
Calculate
32≥5
Calculate
9≥5
Check the inequality
true
x<−5 is the solutionx2=0x3=3
To determine if −5<x<5 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
02≥5
Calculate
0≥5
Check the inequality
false
x<−5 is the solution−5<x<5 is not a solutionx3=3
To determine if x>5 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
More Steps

Evaluate
32≥5
Calculate
9≥5
Check the inequality
true
x<−5 is the solution−5<x<5 is not a solutionx>5 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
x≤−5 is the solutionx≥5 is the solution
Solution
x∈(−∞,−5]∪[5,+∞)
Show Solution
