Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for x
x∈(−∞,−6)∪(6,+∞)
Evaluate
x2>36
Move the expression to the left side
x2−36>0
Rewrite the expression
x2−36=0
Move the constant to the right-hand side and change its sign
x2=0+36
Removing 0 doesn't change the value,so remove it from the expression
x2=36
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±36
Simplify the expression
More Steps

Evaluate
36
Write the number in exponential form with the base of 6
62
Reduce the index of the radical and exponent with 2
6
x=±6
Separate the equation into 2 possible cases
x=6x=−6
Determine the test intervals using the critical values
x<−6−6<x<6x>6
Choose a value form each interval
x1=−7x2=0x3=7
To determine if x<−6 is the solution to the inequality,test if the chosen value x=−7 satisfies the initial inequality
More Steps

Evaluate
(−7)2>36
Calculate
72>36
Calculate
49>36
Check the inequality
true
x<−6 is the solutionx2=0x3=7
To determine if −6<x<6 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
02>36
Calculate
0>36
Check the inequality
false
x<−6 is the solution−6<x<6 is not a solutionx3=7
To determine if x>6 is the solution to the inequality,test if the chosen value x=7 satisfies the initial inequality
More Steps

Evaluate
72>36
Calculate
49>36
Check the inequality
true
x<−6 is the solution−6<x<6 is not a solutionx>6 is the solution
Solution
x∈(−∞,−6)∪(6,+∞)
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