Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,8−1801+43)∪(81801+43,+∞)
Evaluate
9−4x>14x×9−12x2−x
Simplify
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Evaluate
14x×9−12x2−x
Multiply the terms
126x−12x2−x
Subtract the terms
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Evaluate
126x−x
Collect like terms by calculating the sum or difference of their coefficients
(126−1)x
Subtract the numbers
125x
125x−12x2
9−4x>125x−12x2
Move the expression to the left side
9−4x−(125x−12x2)>0
Subtract the terms
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Evaluate
9−4x−(125x−12x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
9−4x−125x+12x2
Subtract the terms
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Evaluate
−4x−125x
Collect like terms by calculating the sum or difference of their coefficients
(−4−125)x
Subtract the numbers
−129x
9−129x+12x2
9−129x+12x2>0
Rewrite the expression
9−129x+12x2=0
Add or subtract both sides
−129x+12x2=−9
Divide both sides
12−129x+12x2=12−9
Evaluate
−443x+x2=−43
Add the same value to both sides
−443x+x2+641849=−43+641849
Simplify the expression
(x−843)2=641801
Take the root of both sides of the equation and remember to use both positive and negative roots
x−843=±641801
Simplify the expression
x−843=±81801
Separate the equation into 2 possible cases
x−843=81801x−843=−81801
Solve the equation
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Evaluate
x−843=81801
Move the constant to the right-hand side and change its sign
x=81801+843
Write all numerators above the common denominator
x=81801+43
x=81801+43x−843=−81801
Solve the equation
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Evaluate
x−843=−81801
Move the constant to the right-hand side and change its sign
x=−81801+843
Write all numerators above the common denominator
x=8−1801+43
x=81801+43x=8−1801+43
Determine the test intervals using the critical values
x<8−1801+438−1801+43<x<81801+43x>81801+43
Choose a value form each interval
x1=−1x2=5x3=12
To determine if x<8−1801+43 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps

Evaluate
9−4(−1)>125(−1)−12(−1)2
Simplify
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Evaluate
9−4(−1)
Simplify
9−(−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
9+4
Add the numbers
13
13>125(−1)−12(−1)2
Simplify
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Evaluate
125(−1)−12(−1)2
Evaluate the power
125(−1)−12×1
Simplify
−125−12×1
Any expression multiplied by 1 remains the same
−125−12
Subtract the numbers
−137
13>−137
Check the inequality
true
x<8−1801+43 is the solutionx2=5x3=12
To determine if 8−1801+43<x<81801+43 is the solution to the inequality,test if the chosen value x=5 satisfies the initial inequality
More Steps

Evaluate
9−4×5>125×5−12×52
Simplify
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Evaluate
9−4×5
Multiply the numbers
9−20
Subtract the numbers
−11
−11>125×5−12×52
Simplify
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Evaluate
125×5−12×52
Multiply the numbers
625−12×52
Multiply the terms
625−300
Subtract the numbers
325
−11>325
Check the inequality
false
x<8−1801+43 is the solution8−1801+43<x<81801+43 is not a solutionx3=12
To determine if x>81801+43 is the solution to the inequality,test if the chosen value x=12 satisfies the initial inequality
More Steps

Evaluate
9−4×12>125×12−12×122
Simplify
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Evaluate
9−4×12
Multiply the numbers
9−48
Subtract the numbers
−39
−39>125×12−12×122
Simplify
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Evaluate
125×12−12×122
Multiply the numbers
1500−12×122
Calculate the product
1500−123
Evaluate the power
1500−1728
Subtract the numbers
−228
−39>−228
Check the inequality
true
x<8−1801+43 is the solution8−1801+43<x<81801+43 is not a solutionx>81801+43 is the solution
Solution
x∈(−∞,8−1801+43)∪(81801+43,+∞)
Show Solution
