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
−5≤x≤5
Alternative Form
x∈[−5,5]
Evaluate
(x−5)(x+5)≤0
Rewrite the expression
(x−5)(x+5)=0
Separate the equation into 2 possible cases
x−5=0x+5=0
Solve the equation
More Steps
Evaluate
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=5x+5=0
Solve the equation
More Steps
Evaluate
x+5=0
Move the constant to the right-hand side and change its sign
x=0−5
Removing 0 doesn't change the value,so remove it from the expression
x=−5
x=5x=−5
Determine the test intervals using the critical values
x<−5−5<x<5x>5
Choose a value form each interval
x1=−6x2=0x3=6
To determine if x<−5 is the solution to the inequality,test if the chosen value x=−6 satisfies the initial inequality
More Steps
Evaluate
(−6−5)(−6+5)≤0
Simplify
More Steps
Evaluate
(−6−5)(−6+5)
Subtract the numbers
(−11)(−6+5)
Remove the parentheses
−11(−6+5)
Add the numbers
−11(−1)
Simplify
11
11≤0
Check the inequality
false
x<−5 is not a solutionx2=0x3=6
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
(0−5)(0+5)≤0
Simplify
More Steps
Evaluate
(0−5)(0+5)
Removing 0 doesn't change the value,so remove it from the expression
(−5)(0+5)
Remove the parentheses
−5(0+5)
Removing 0 doesn't change the value,so remove it from the expression
−5×5
Multiply the numbers
−25
−25≤0
Check the inequality
true
x<−5 is not a solution−5<x<5 is the solutionx3=6
To determine if x>5 is the solution to the inequality,test if the chosen value x=6 satisfies the initial inequality
More Steps
Evaluate
(6−5)(6+5)≤0
Simplify
More Steps
Evaluate
(6−5)(6+5)
Subtract the numbers
1×(6+5)
Add the numbers
1×11
Any expression multiplied by 1 remains the same
11
11≤0
Check the inequality
false
x<−5 is not a solution−5<x<5 is the solutionx>5 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−5≤x≤5 is the solution
Solution
−5≤x≤5
Alternative Form
x∈[−5,5]
Show Solution
