Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
−2<x<8
Alternative Form
x∈(−2,8)
Evaluate
−1<∣x−3∣<5
Separate into two inequalities
{−1<∣x−3∣∣x−3∣<5
Since the left-hand side is always negative,and the right-hand side is always positive or 0,the statement is true for any value of x
{x∈R∣x−3∣<5
Solve the inequality
More Steps
Evaluate
∣x−3∣<5
Separate the inequality into 2 possible cases
{x−3<5x−3>−5
Solve the inequality for x
More Steps
Evaluate
x−3<5
Move the constant to the right side
x<5+3
Add the numbers
x<8
{x<8x−3>−5
Solve the inequality for x
More Steps
Evaluate
x−3>−5
Move the constant to the right side
x>−5+3
Add the numbers
x>−2
{x<8x>−2
Find the intersection
−2<x<8
{x∈R−2<x<8
Solution
−2<x<8
Alternative Form
x∈(−2,8)
Show Solution
