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 m
−2<m<2
Alternative Form
m∈(−2,2)
Evaluate
m2−4<0
Rewrite the expression
m2−4=0
Move the constant to the right-hand side and change its sign
m2=0+4
Removing 0 doesn't change the value,so remove it from the expression
m2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
m=±4
Simplify the expression
More Steps
Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
m=±2
Separate the equation into 2 possible cases
m=2m=−2
Determine the test intervals using the critical values
m<−2−2<m<2m>2
Choose a value form each interval
m1=−3m2=0m3=3
To determine if m<−2 is the solution to the inequality,test if the chosen value m=−3 satisfies the initial inequality
More Steps
Evaluate
(−3)2−4<0
Subtract the numbers
More Steps
Evaluate
(−3)2−4
Simplify
32−4
Evaluate the power
9−4
Subtract the numbers
5
5<0
Check the inequality
false
m<−2 is not a solutionm2=0m3=3
To determine if −2<m<2 is the solution to the inequality,test if the chosen value m=0 satisfies the initial inequality
More Steps
Evaluate
02−4<0
Simplify
More Steps
Evaluate
02−4
Calculate
0−4
Removing 0 doesn't change the value,so remove it from the expression
−4
−4<0
Check the inequality
true
m<−2 is not a solution−2<m<2 is the solutionm3=3
To determine if m>2 is the solution to the inequality,test if the chosen value m=3 satisfies the initial inequality
More Steps
Evaluate
32−4<0
Subtract the numbers
More Steps
Evaluate
32−4
Evaluate the power
9−4
Subtract the numbers
5
5<0
Check the inequality
false
m<−2 is not a solution−2<m<2 is the solutionm>2 is not a solution
Solution
−2<m<2
Alternative Form
m∈(−2,2)
Show Solution
