Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,−6)∪(6,+∞)
Evaluate
91x×x−32>0
Multiply the terms
91x2−32>0
Rewrite the expression
91x2−32=0
Move the constant to the right-hand side and change its sign
91x2=0+32
Add the terms
91x2=32
Multiply by the reciprocal
91x2×9=32×9
Multiply
x2=32×9
Multiply
More Steps

Evaluate
32×9
Reduce the numbers
2×3
Multiply the numbers
6
x2=6
Take the root of both sides of the equation and remember to use both positive and negative roots
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=−3x2=0x3=3
To determine if x<−6 is the solution to the inequality,test if the chosen value x=−3 satisfies the initial inequality
More Steps

Evaluate
91(−3)2−32>0
Simplify
More Steps

Evaluate
91(−3)2−32
Multiply the numbers
1−32
Reduce fractions to a common denominator
33−32
Write all numerators above the common denominator
33−2
Subtract the numbers
31
31>0
Calculate
0.3˙>0
Check the inequality
true
x<−6 is the solutionx2=0x3=3
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
91×02−32>0
Simplify
More Steps

Evaluate
91×02−32
Calculate
91×0−32
Any expression multiplied by 0 equals 0
0−32
Removing 0 doesn't change the value,so remove it from the expression
−32
−32>0
Calculate
−0.6˙>0
Check the inequality
false
x<−6 is the solution−6<x<6 is not a solutionx3=3
To determine if x>6 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
More Steps

Evaluate
91×32−32>0
Simplify
More Steps

Evaluate
91×32−32
Multiply the numbers
1−32
Reduce fractions to a common denominator
33−32
Write all numerators above the common denominator
33−2
Subtract the numbers
31
31>0
Calculate
0.3˙>0
Check the inequality
true
x<−6 is the solution−6<x<6 is not a solutionx>6 is the solution
Solution
x∈(−∞,−6)∪(6,+∞)
Show Solution
