Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
x>251
Alternative Form
x∈(251,+∞)
Evaluate
−3x2×8x<(x−1)x2
Multiply
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Evaluate
−3x2×8x
Multiply the terms
−24x2×x
Multiply the terms with the same base by adding their exponents
−24x2+1
Add the numbers
−24x3
−24x3<(x−1)x2
Multiply the terms
−24x3<x2(x−1)
Move the expression to the left side
−24x3−x2(x−1)<0
Subtract the terms
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Evaluate
−24x3−x2(x−1)
Expand the expression
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Calculate
x2(x−1)
Apply the distributive property
x2×x−x2×1
Multiply the terms
x3−x2×1
Any expression multiplied by 1 remains the same
x3−x2
−24x3−(x3−x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−24x3−x3+x2
Subtract the terms
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Evaluate
−24x3−x3
Collect like terms by calculating the sum or difference of their coefficients
(−24−1)x3
Subtract the numbers
−25x3
−25x3+x2
−25x3+x2<0
Rewrite the expression
−25x3+x2=0
Factor the expression
x2(−25x+1)=0
Separate the equation into 2 possible cases
x2=0−25x+1=0
The only way a power can be 0 is when the base equals 0
x=0−25x+1=0
Solve the equation
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Evaluate
−25x+1=0
Move the constant to the right-hand side and change its sign
−25x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−25x=−1
Change the signs on both sides of the equation
25x=1
Divide both sides
2525x=251
Divide the numbers
x=251
x=0x=251
Determine the test intervals using the critical values
x<00<x<251x>251
Choose a value form each interval
x1=−1x2=501x3=1
To determine if x<0 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
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Evaluate
−24(−1)3<(−1)2(−1−1)
Multiply the terms
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Evaluate
−24(−1)3
Evaluate the power
−24(−1)
Multiply the numbers
24
24<(−1)2(−1−1)
Simplify
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Evaluate
(−1)2(−1−1)
Subtract the numbers
(−1)2(−2)
Evaluate the power
1×(−2)
Any expression multiplied by 1 remains the same
−2
24<−2
Check the inequality
false
x<0 is not a solutionx2=501x3=1
To determine if 0<x<251 is the solution to the inequality,test if the chosen value x=501 satisfies the initial inequality
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Evaluate
−24(501)3<(501)2(501−1)
Simplify
−24×5031<(501)2(501−1)
Simplify
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Evaluate
(501)2(501−1)
Subtract the numbers
(501)2(−5049)
Evaluate the power
5021×(−5049)
Multiplying or dividing an odd number of negative terms equals a negative
−5021×5049
To multiply the fractions,multiply the numerators and denominators separately
−502×5049
Multiply the numbers
−50349
−24×5031<−50349
Calculate
−0.000192<−50349
Calculate
−0.000192<−0.000392
Check the inequality
false
x<0 is not a solution0<x<251 is not a solutionx3=1
To determine if x>251 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
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Evaluate
−24×13<12×(1−1)
Simplify
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Evaluate
−24×13
1 raised to any power equals to 1
−24×1
Any expression multiplied by 1 remains the same
−24
−24<12×(1−1)
Simplify
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Evaluate
12×(1−1)
Subtract the numbers
12×0
Any expression multiplied by 0 equals 0
0
−24<0
Check the inequality
true
x<0 is not a solution0<x<251 is not a solutionx>251 is the solution
Solution
x>251
Alternative Form
x∈(251,+∞)
Show Solution
