Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(21,2)∪(3,29)
Evaluate
1<∣2x−5∣<4
Separate into two inequalities
{1<∣2x−5∣∣2x−5∣<4
Solve the inequality
More Steps
Evaluate
1<∣2x−5∣
Swap the sides of the inequality
∣2x−5∣>1
Separate the inequality into 2 possible cases
2x−5>12x−5<−1
Solve the inequality for x
More Steps
Evaluate
2x−5>1
Move the constant to the right side
2x>1+5
Add the numbers
2x>6
Divide both sides
22x>26
Divide the numbers
x>26
Divide the numbers
x>3
x>32x−5<−1
Solve the inequality for x
More Steps
Evaluate
2x−5<−1
Move the constant to the right side
2x<−1+5
Add the numbers
2x<4
Divide both sides
22x<24
Divide the numbers
x<24
Divide the numbers
x<2
x>3x<2
Find the union
x∈(−∞,2)∪(3,+∞)
{x∈(−∞,2)∪(3,+∞)∣2x−5∣<4
Solve the inequality
More Steps
Evaluate
∣2x−5∣<4
Separate the inequality into 2 possible cases
{2x−5<42x−5>−4
Solve the inequality for x
More Steps
Evaluate
2x−5<4
Move the constant to the right side
2x<4+5
Add the numbers
2x<9
Divide both sides
22x<29
Divide the numbers
x<29
{x<292x−5>−4
Solve the inequality for x
More Steps
Evaluate
2x−5>−4
Move the constant to the right side
2x>−4+5
Add the numbers
2x>1
Divide both sides
22x>21
Divide the numbers
x>21
{x<29x>21
Find the intersection
21<x<29
{x∈(−∞,2)∪(3,+∞)21<x<29
Solution
x∈(21,2)∪(3,29)
Show Solution
