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
−7≤x≤7
Alternative Form
x∈[−7,7]
Evaluate
x4−6x2−7≤0
Rewrite the expression
x4−6x2−7=0
Factor the expression
(x2−7)(x2+1)=0
Separate the equation into 2 possible cases
x2−7=0x2+1=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
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±7
Separate the equation into 2 possible cases
x=7x=−7
x=7x=−7x2+1=0
Solve the equation
More Steps
Evaluate
x2+1=0
Move the constant to the right-hand side and change its sign
x2=0−1
Removing 0 doesn't change the value,so remove it from the expression
x2=−1
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=7x=−7x∈/R
Find the union
x=7x=−7
Determine the test intervals using the critical values
x<−7−7<x<7x>7
Choose a value form each interval
x1=−4x2=0x3=4
To determine if x<−7 is the solution to the inequality,test if the chosen value x=−4 satisfies the initial inequality
More Steps
Evaluate
(−4)4−6(−4)2−7≤0
Simplify
More Steps
Evaluate
(−4)4−6(−4)2−7
Multiply the terms
(−4)4−96−7
Evaluate the power
256−96−7
Subtract the numbers
153
153≤0
Check the inequality
false
x<−7 is not a solutionx2=0x3=4
To determine if −7<x<7 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
04−6×02−7≤0
Simplify
More Steps
Evaluate
04−6×02−7
Calculate
0−6×02−7
Calculate
0−6×0−7
Any expression multiplied by 0 equals 0
0−0−7
Removing 0 doesn't change the value,so remove it from the expression
−7
−7≤0
Check the inequality
true
x<−7 is not a solution−7<x<7 is the solutionx3=4
To determine if x>7 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps
Evaluate
44−6×42−7≤0
Simplify
More Steps
Evaluate
44−6×42−7
Multiply the terms
44−96−7
Evaluate the power
256−96−7
Subtract the numbers
153
153≤0
Check the inequality
false
x<−7 is not a solution−7<x<7 is the solutionx>7 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−7≤x≤7 is the solution
Solution
−7≤x≤7
Alternative Form
x∈[−7,7]
Show Solution
