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
−3≤x≤3
Alternative Form
x∈[−3,3]
Evaluate
x4−2x2−63≤0
Rewrite the expression
x4−2x2−63=0
Factor the expression
(x−3)(x+3)(x2+7)=0
Separate the equation into 3 possible cases
x−3=0x+3=0x2+7=0
Solve the equation
More Steps
Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x+3=0x2+7=0
Solve the equation
More Steps
Evaluate
x+3=0
Move the constant to the right-hand side and change its sign
x=0−3
Removing 0 doesn't change the value,so remove it from the expression
x=−3
x=3x=−3x2+7=0
Solve the equation
More Steps
Evaluate
x2+7=0
Move the constant to the right-hand side and change its sign
x2=0−7
Removing 0 doesn't change the value,so remove it from the expression
x2=−7
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x
x∈/R
x=3x=−3x∈/R
Find the union
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
(−4)4−2(−4)2−63≤0
Simplify
More Steps
Evaluate
(−4)4−2(−4)2−63
Multiply the terms
(−4)4−32−63
Evaluate the power
256−32−63
Subtract the numbers
161
161≤0
Check the inequality
false
x<−3 is not a 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
04−2×02−63≤0
Simplify
More Steps
Evaluate
04−2×02−63
Calculate
0−2×02−63
Calculate
0−2×0−63
Any expression multiplied by 0 equals 0
0−0−63
Removing 0 doesn't change the value,so remove it from the expression
−63
−63≤0
Check the inequality
true
x<−3 is not a solution−3<x<3 is the 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
44−2×42−63≤0
Simplify
More Steps
Evaluate
44−2×42−63
Multiply the terms
44−32−63
Evaluate the power
256−32−63
Subtract the numbers
161
161≤0
Check the inequality
false
x<−3 is not a solution−3<x<3 is the solutionx>3 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−3≤x≤3 is the solution
Solution
−3≤x≤3
Alternative Form
x∈[−3,3]
Show Solution
