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∈(−∞,−1]∪[1,+∞)
Evaluate
x2×1≥1
Simplify
More Steps
Evaluate
x2×1
Any expression multiplied by 1 remains the same
x2
When the expression in absolute value bars is not negative, remove the bars
x2
x2≥1
Move the expression to the left side
x2−1≥0
Rewrite the expression
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
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±1
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
Determine the test intervals using the critical values
x<−1−1<x<1x>1
Choose a value form each interval
x1=−2x2=0x3=2
To determine if x<−1 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
(−2)2≥1
Calculate
22≥1
Calculate
4≥1
Check the inequality
true
x<−1 is the solutionx2=0x3=2
To determine if −1<x<1 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
02≥1
Calculate
0≥1
Check the inequality
false
x<−1 is the solution−1<x<1 is not a solutionx3=2
To determine if x>1 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
22≥1
Calculate
4≥1
Check the inequality
true
x<−1 is the solution−1<x<1 is not a solutionx>1 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
x≤−1 is the solutionx≥1 is the solution
Solution
x∈(−∞,−1]∪[1,+∞)
Show Solution
