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
−1<x<3
Alternative Form
x∈(−1,3)
Evaluate
(x−1)2<4
Move the expression to the left side
(x−1)2−4<0
Subtract the terms
More Steps
Evaluate
(x−1)2−4
Expand the expression
x2−2x+1−4
Subtract the numbers
x2−2x−3
x2−2x−3<0
Rewrite the expression
x2−2x−3=0
Factor the expression
More Steps
Evaluate
x2−2x−3
Rewrite the expression
x2+(1−3)x−3
Calculate
x2+x−3x−3
Rewrite the expression
x×x+x−3x−3
Factor out x from the expression
x(x+1)−3x−3
Factor out −3 from the expression
x(x+1)−3(x+1)
Factor out x+1 from the expression
(x−3)(x+1)
(x−3)(x+1)=0
When the product of factors equals 0,at least one factor is 0
x−3=0x+1=0
Solve the equation for x
More Steps
Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x+1=0
Solve the equation for x
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=3x=−1
Determine the test intervals using the critical values
x<−1−1<x<3x>3
Choose a value form each interval
x1=−2x2=1x3=4
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
(−2−1)2<4
Subtract the numbers
(−3)2<4
Calculate
32<4
Calculate
9<4
Check the inequality
false
x<−1 is not a solutionx2=1x3=4
To determine if −1<x<3 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps
Evaluate
(1−1)2<4
Simplify
More Steps
Evaluate
(1−1)2
Subtract the numbers
02
Calculate
0
0<4
Check the inequality
true
x<−1 is not a solution−1<x<3 is the solutionx3=4
To determine if x>3 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps
Evaluate
(4−1)2<4
Subtract the numbers
32<4
Calculate
9<4
Check the inequality
false
x<−1 is not a solution−1<x<3 is the solutionx>3 is not a solution
Solution
−1<x<3
Alternative Form
x∈(−1,3)
Show Solution
