Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
−22<x<22
Alternative Form
x∈(−22,22)
Evaluate
2x2−1<0
Rewrite the expression
2x2−1=0
Move the constant to the right-hand side and change its sign
2x2=0+1
Removing 0 doesn't change the value,so remove it from the expression
2x2=1
Divide both sides
22x2=21
Divide the numbers
x2=21
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±21
Simplify the expression
More Steps

Evaluate
21
To take a root of a fraction,take the root of the numerator and denominator separately
21
Simplify the radical expression
21
Multiply by the Conjugate
2×22
When a square root of an expression is multiplied by itself,the result is that expression
22
x=±22
Separate the equation into 2 possible cases
x=22x=−22
Determine the test intervals using the critical values
x<−22−22<x<22x>22
Choose a value form each interval
x1=−2x2=0x3=2
To determine if x<−22 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps

Evaluate
2(−2)2−1<0
Simplify
More Steps

Evaluate
2(−2)2−1
Multiply the terms
23−1
Evaluate the power
8−1
Subtract the numbers
7
7<0
Check the inequality
false
x<−22 is not a solutionx2=0x3=2
To determine if −22<x<22 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
2×02−1<0
Simplify
More Steps

Evaluate
2×02−1
Calculate
2×0−1
Any expression multiplied by 0 equals 0
0−1
Removing 0 doesn't change the value,so remove it from the expression
−1
−1<0
Check the inequality
true
x<−22 is not a solution−22<x<22 is the solutionx3=2
To determine if x>22 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps

Evaluate
2×22−1<0
Simplify
More Steps

Evaluate
2×22−1
Calculate the product
23−1
Evaluate the power
8−1
Subtract the numbers
7
7<0
Check the inequality
false
x<−22 is not a solution−22<x<22 is the solutionx>22 is not a solution
Solution
−22<x<22
Alternative Form
x∈(−22,22)
Show Solution
