Question
Solve the inequality
x>233−3
Alternative Form
x∈(233−3,+∞)
Evaluate
x2−x−6>0x2−4x<0
Separate into two inequalities
{x2−x−6>0×x2−4x0×x2−4x<0
Solve the inequality
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Evaluate
x2−x−6>0×x2−4x
Simplify
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Evaluate
0×x2−4x
Any expression multiplied by 0 equals 0
0−4x
Removing 0 doesn't change the value,so remove it from the expression
−4x
x2−x−6>−4x
Move the expression to the left side
x2−x−6−(−4x)>0
Subtract the terms
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Evaluate
x2−x−6−(−4x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2−x−6+4x
Add the terms
x2+3x−6
x2+3x−6>0
Move the constant to the right side
x2+3x>0−(−6)
Add the terms
x2+3x>6
Add the same value to both sides
x2+3x+49>6+49
Evaluate
x2+3x+49>433
Evaluate
(x+23)2>433
Take the 2-th root on both sides of the inequality
(x+23)2>433
Calculate
x+23>233
Separate the inequality into 2 possible cases
x+23>233x+23<−233
Calculate
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Evaluate
x+23>233
Move the constant to the right side
x>233−23
Write all numerators above the common denominator
x>233−3
x>233−3x+23<−233
Calculate
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Evaluate
x+23<−233
Move the constant to the right side
x<−233−23
Subtract the numbers
x<−233+3
x>233−3x<−233+3
Find the union
x∈(−∞,−233+3)∪(233−3,+∞)
{x∈(−∞,−233+3)∪(233−3,+∞)0×x2−4x<0
Solve the inequality
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Evaluate
0×x2−4x<0
Simplify
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Evaluate
0×x2−4x
Any expression multiplied by 0 equals 0
0−4x
Removing 0 doesn't change the value,so remove it from the expression
−4x
−4x<0
Change the signs on both sides of the inequality and flip the inequality sign
4x>0
Rewrite the expression
x>0
{x∈(−∞,−233+3)∪(233−3,+∞)x>0
Solution
x>233−3
Alternative Form
x∈(233−3,+∞)
Show Solution
