Algebra
Calculus
Trigonometry
Matrix
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∈(−∞,−3)∪(3,+∞)
Evaluate
9−x2<0
Rewrite the expression
9−x2=0
Move the constant to the right-hand side and change its sign
−x2=0−9
Removing 0 doesn't change the value,so remove it from the expression
−x2=−9
Change the signs on both sides of the equation
x2=9
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±9
Simplify the expression
More Steps
Evaluate
9
Write the number in exponential form with the base of 3
32
Reduce the index of the radical and exponent with 2
3
x=±3
Separate the equation into 2 possible cases
x=3x=−3
Determine the test intervals using the critical values
x<−3−3<x<3x>3
Choose a value form each interval
x1=−4x2=0x3=4
To determine if x<−3 is the solution to the inequality,test if the chosen value x=−4 satisfies the initial inequality
More Steps
Evaluate
9−(−4)2<0
Subtract the numbers
More Steps
Simplify
9−(−4)2
Rewrite the expression
9−42
Evaluate the power
9−16
Subtract the numbers
−7
−7<0
Check the inequality
true
x<−3 is the solutionx2=0x3=4
To determine if −3<x<3 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
9−02<0
Simplify
More Steps
Evaluate
9−02
Calculate
9−0
Removing 0 doesn't change the value,so remove it from the expression
9
9<0
Check the inequality
false
x<−3 is the solution−3<x<3 is not a solutionx3=4
To determine if x>3 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps
Evaluate
9−42<0
Subtract the numbers
More Steps
Evaluate
9−42
Evaluate the power
9−16
Subtract the numbers
−7
−7<0
Check the inequality
true
x<−3 is the solution−3<x<3 is not a solutionx>3 is the solution
Solution
x∈(−∞,−3)∪(3,+∞)
Show Solution
