Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−∞,0)∪(1,+∞)
Evaluate
∣3x−2∣>2−x
Rearrange the terms
∣3x−2∣+x>2
Separate the inequality into 2 possible cases
3x−2+x>2,3x−2≥0−(3x−2)+x>2,3x−2<0
Evaluate
More Steps
Evaluate
3x−2+x>2
Simplify the expression
4x−2>2
Move the expression to the left side
4x−2−2>0
Calculate
4x−4>0
Move the constant to the right side
4x>0+4
Removing 0 doesn't change the value,so remove it from the expression
4x>4
Divide both sides
44x>44
Divide the numbers
x>44
Divide the numbers
More Steps
Evaluate
44
Reduce the numbers
11
Calculate
1
x>1
x>1,3x−2≥0−(3x−2)+x>2,3x−2<0
Evaluate
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Evaluate
3x−2≥0
Move the constant to the right side
3x≥0+2
Removing 0 doesn't change the value,so remove it from the expression
3x≥2
Divide both sides
33x≥32
Divide the numbers
x≥32
x>1,x≥32−(3x−2)+x>2,3x−2<0
Evaluate
More Steps
Evaluate
−(3x−2)+x>2
Remove the parentheses
−3x+2+x>2
Simplify the expression
−2x+2>2
Move the expression to the left side
−2x+2−2>0
Calculate
−2x+0>0
Evaluate
−2x>0
Change the signs on both sides of the inequality and flip the inequality sign
2x<0
Rewrite the expression
x<0
x>1,x≥32x<0,3x−2<0
Evaluate
More Steps
Evaluate
3x−2<0
Move the constant to the right side
3x<0+2
Removing 0 doesn't change the value,so remove it from the expression
3x<2
Divide both sides
33x<32
Divide the numbers
x<32
x>1,x≥32x<0,x<32
Find the intersection
x>1x<0,x<32
Find the intersection
x>1x<0
Solution
x∈(−∞,0)∪(1,+∞)
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