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
−1≤x<1
Alternative Form
x∈[−1,1)
Evaluate
x−12x×1≤1
Find the domain
More Steps
Evaluate
x−1=0
Move the constant to the right side
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x−12x×1≤1,x=1
Multiply the terms
x−12x≤1
Move the expression to the left side
x−12x−1≤0
Subtract the terms
More Steps
Evaluate
x−12x−1
Reduce fractions to a common denominator
x−12x−x−1x−1
Write all numerators above the common denominator
x−12x−(x−1)
Subtract the terms
More Steps
Evaluate
2x−(x−1)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2x−x+1
Subtract the terms
x+1
x−1x+1
x−1x+1≤0
Set the numerator and denominator of x−1x+1 equal to 0 to find the values of x where sign changes may occur
x+1=0x−1=0
Calculate
More Steps
Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=−1x−1=0
Calculate
More Steps
Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
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
−2−12(−2)≤1
Simplify
More Steps
Evaluate
−2−12(−2)
Multiply the numbers
−2−1−4
Subtract the numbers
−3−4
Cancel out the common factor −1
34
34≤1
Calculate
1.3˙≤1
Check the inequality
false
x<−1 is not a 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
0−12×0≤1
Any expression multiplied by 0 equals 0
0−10≤1
Simplify
More Steps
Evaluate
0−10
Removing 0 doesn't change the value,so remove it from the expression
−10
Divide the terms
0
0≤1
Check the inequality
true
x<−1 is not a solution−1<x<1 is the 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
2−12×2≤1
Simplify
More Steps
Evaluate
2−12×2
Multiply the numbers
2−14
Subtract the numbers
14
Divide the terms
4
4≤1
Check the inequality
false
x<−1 is not a solution−1<x<1 is the solutionx>1 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−1≤x<1 is the solution
The final solution of the original inequality is −1≤x<1
−1≤x<1
Check if the solution is in the defined range
−1≤x<1,x=1
Solution
−1≤x<1
Alternative Form
x∈[−1,1)
Show Solution
