Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
−19<x<19
Alternative Form
x∈(−19,19)
Evaluate
x2<19
Move the expression to the left side
x2−19<0
Rewrite the expression
x2−19=0
Move the constant to the right-hand side and change its sign
x2=0+19
Removing 0 doesn't change the value,so remove it from the expression
x2=19
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±19
Separate the equation into 2 possible cases
x=19x=−19
Determine the test intervals using the critical values
x<−19−19<x<19x>19
Choose a value form each interval
x1=−5x2=0x3=5
To determine if x<−19 is the solution to the inequality,test if the chosen value x=−5 satisfies the initial inequality
More Steps

Evaluate
(−5)2<19
Calculate
52<19
Calculate
25<19
Check the inequality
false
x<−19 is not a solutionx2=0x3=5
To determine if −19<x<19 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
02<19
Calculate
0<19
Check the inequality
true
x<−19 is not a solution−19<x<19 is the solutionx3=5
To determine if x>19 is the solution to the inequality,test if the chosen value x=5 satisfies the initial inequality
More Steps

Evaluate
52<19
Calculate
25<19
Check the inequality
false
x<−19 is not a solution−19<x<19 is the solutionx>19 is not a solution
Solution
−19<x<19
Alternative Form
x∈(−19,19)
Show Solution
