Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−∞,−1)∪(2,+∞)
Evaluate
∣x−1∣∣x×1∣>2
Simplify
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Evaluate
∣x−1∣∣x×1∣
Any expression multiplied by 1 remains the same
∣x−1∣∣x∣
Multiply the terms
∣x(x−1)∣
∣x(x−1)∣>2
Separate the inequality into 2 possible cases
x(x−1)>2x(x−1)<−2
Solve the inequality for x
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Evaluate
x(x−1)>2
Expand the expression
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Evaluate
x(x−1)
Apply the distributive property
x×x−x×1
Multiply the terms
x2−x×1
Any expression multiplied by 1 remains the same
x2−x
x2−x>2
Add the same value to both sides
x2−x+41>2+41
Evaluate
x2−x+41>49
Evaluate
(x−21)2>49
Take the 2-th root on both sides of the inequality
(x−21)2>49
Calculate
x−21>23
Separate the inequality into 2 possible cases
x−21>23x−21<−23
Calculate
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Evaluate
x−21>23
Move the constant to the right side
x>23+21
Add the numbers
x>2
x>2x−21<−23
Calculate
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Evaluate
x−21<−23
Move the constant to the right side
x<−23+21
Add the numbers
x<−1
x>2x<−1
Find the union
x∈(−∞,−1)∪(2,+∞)
x∈(−∞,−1)∪(2,+∞)x(x−1)<−2
Solve the inequality for x
More Steps
Evaluate
x(x−1)<−2
Expand the expression
More Steps
Evaluate
x(x−1)
Apply the distributive property
x×x−x×1
Multiply the terms
x2−x×1
Any expression multiplied by 1 remains the same
x2−x
x2−x<−2
Add the same value to both sides
x2−x+41<−2+41
Evaluate
x2−x+41<−47
Evaluate
(x−21)2<−47
Calculate
x∈/R
x∈(−∞,−1)∪(2,+∞)x∈/R
Solution
x∈(−∞,−1)∪(2,+∞)
Show Solution
