Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−3,−1)∪(2,4)
Evaluate
3<∣2x−1∣<7
Separate into two inequalities
{3<∣2x−1∣∣2x−1∣<7
Solve the inequality
More Steps
Evaluate
3<∣2x−1∣
Swap the sides of the inequality
∣2x−1∣>3
Separate the inequality into 2 possible cases
2x−1>32x−1<−3
Solve the inequality for x
More Steps
Evaluate
2x−1>3
Move the constant to the right side
2x>3+1
Add the numbers
2x>4
Divide both sides
22x>24
Divide the numbers
x>24
Divide the numbers
x>2
x>22x−1<−3
Solve the inequality for x
More Steps
Evaluate
2x−1<−3
Move the constant to the right side
2x<−3+1
Add the numbers
2x<−2
Divide both sides
22x<2−2
Divide the numbers
x<2−2
Divide the numbers
x<−1
x>2x<−1
Find the union
x∈(−∞,−1)∪(2,+∞)
{x∈(−∞,−1)∪(2,+∞)∣2x−1∣<7
Solve the inequality
More Steps
Evaluate
∣2x−1∣<7
Separate the inequality into 2 possible cases
{2x−1<72x−1>−7
Solve the inequality for x
More Steps
Evaluate
2x−1<7
Move the constant to the right side
2x<7+1
Add the numbers
2x<8
Divide both sides
22x<28
Divide the numbers
x<28
Divide the numbers
x<4
{x<42x−1>−7
Solve the inequality for x
More Steps
Evaluate
2x−1>−7
Move the constant to the right side
2x>−7+1
Add the numbers
2x>−6
Divide both sides
22x>2−6
Divide the numbers
x>2−6
Divide the numbers
x>−3
{x<4x>−3
Find the intersection
−3<x<4
{x∈(−∞,−1)∪(2,+∞)−3<x<4
Solution
x∈(−3,−1)∪(2,4)
Show Solution
