Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,−15)∪(15,+∞)
Evaluate
x2−8>7
Move the expression to the left side
x2−8−7>0
Subtract the numbers
x2−15>0
Rewrite the expression
x2−15=0
Move the constant to the right-hand side and change its sign
x2=0+15
Removing 0 doesn't change the value,so remove it from the expression
x2=15
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±15
Separate the equation into 2 possible cases
x=15x=−15
Determine the test intervals using the critical values
x<−15−15<x<15x>15
Choose a value form each interval
x1=−5x2=0x3=5
To determine if x<−15 is the solution to the inequality,test if the chosen value x=−5 satisfies the initial inequality
More Steps

Evaluate
(−5)2−8>7
Subtract the numbers
More Steps

Evaluate
(−5)2−8
Simplify
52−8
Evaluate the power
25−8
Subtract the numbers
17
17>7
Check the inequality
true
x<−15 is the solutionx2=0x3=5
To determine if −15<x<15 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
02−8>7
Simplify
More Steps

Evaluate
02−8
Calculate
0−8
Removing 0 doesn't change the value,so remove it from the expression
−8
−8>7
Check the inequality
false
x<−15 is the solution−15<x<15 is not a solutionx3=5
To determine if x>15 is the solution to the inequality,test if the chosen value x=5 satisfies the initial inequality
More Steps

Evaluate
52−8>7
Subtract the numbers
More Steps

Evaluate
52−8
Evaluate the power
25−8
Subtract the numbers
17
17>7
Check the inequality
true
x<−15 is the solution−15<x<15 is not a solutionx>15 is the solution
Solution
x∈(−∞,−15)∪(15,+∞)
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