Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
x∈(−54125,0)∪(0,54125)
Evaluate
x2−5x6>0
Rewrite the expression
x2−5x6=0
Factor the expression
x2(1−5x4)=0
Separate the equation into 2 possible cases
x2=01−5x4=0
The only way a power can be 0 is when the base equals 0
x=01−5x4=0
Solve the equation
More Steps
Evaluate
1−5x4=0
Move the constant to the right-hand side and change its sign
−5x4=0−1
Removing 0 doesn't change the value,so remove it from the expression
−5x4=−1
Change the signs on both sides of the equation
5x4=1
Divide both sides
55x4=51
Divide the numbers
x4=51
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±451
Simplify the expression
More Steps
Evaluate
451
To take a root of a fraction,take the root of the numerator and denominator separately
4541
Simplify the radical expression
451
Multiply by the Conjugate
45×453453
Simplify
45×4534125
Multiply the numbers
54125
x=±54125
Separate the equation into 2 possible cases
x=54125x=−54125
x=0x=54125x=−54125
Determine the test intervals using the critical values
x<−54125−54125<x<00<x<54125x>54125
Choose a value form each interval
x1=−2x2=−104125x3=104125x4=2
To determine if x<−54125 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
(−2)2−5(−2)6>0
Simplify
More Steps
Evaluate
(−2)2−5(−2)6
Multiply the terms
(−2)2−320
Rewrite the expression
22−320
Evaluate the power
4−320
Subtract the numbers
−316
−316>0
Check the inequality
false
x<−54125 is not a solutionx2=−104125x3=104125x4=2
To determine if −54125<x<0 is the solution to the inequality,test if the chosen value x=−104125 satisfies the initial inequality
More Steps
Evaluate
(−104125)2−5(−104125)6>0
Simplify
More Steps
Evaluate
(−104125)2−5(−104125)6
Simplify
(−104125)2−5×106545
Rewrite the expression
205−5×106545
Rewrite the expression
205−106555
Reduce fractions to a common denominator
20×500005×50000−106555
Multiply the numbers
10000005×50000−106555
Rewrite the expression
1065×50000−106555
Write all numerators above the common denominator
1065×50000−555
Use the commutative property to reorder the terms
106500005−555
Subtract the numbers
106468755
Rewrite the expression
10615625×35
Rewrite the expression
56×2615625×35
Rewrite the expression
56×2656×35
Reduce the fraction
2635
2635>0
Calculate
0.104816>0
Check the inequality
true
x<−54125 is not a solution−54125<x<0 is the solutionx3=104125x4=2
To determine if 0<x<54125 is the solution to the inequality,test if the chosen value x=104125 satisfies the initial inequality
More Steps
Evaluate
(104125)2−5(104125)6>0
Simplify
More Steps
Evaluate
(104125)2−5(104125)6
Simplify
(104125)2−5×106545
Rewrite the expression
205−5×106545
Rewrite the expression
205−106555
Reduce fractions to a common denominator
20×500005×50000−106555
Multiply the numbers
10000005×50000−106555
Rewrite the expression
1065×50000−106555
Write all numerators above the common denominator
1065×50000−555
Use the commutative property to reorder the terms
106500005−555
Subtract the numbers
106468755
Rewrite the expression
10615625×35
Rewrite the expression
56×2615625×35
Rewrite the expression
56×2656×35
Reduce the fraction
2635
2635>0
Calculate
0.104816>0
Check the inequality
true
x<−54125 is not a solution−54125<x<0 is the solution0<x<54125 is the solutionx4=2
To determine if x>54125 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
22−5×26>0
Simplify
More Steps
Evaluate
22−5×26
Multiply the terms
22−320
Evaluate the power
4−320
Subtract the numbers
−316
−316>0
Check the inequality
false
x<−54125 is not a solution−54125<x<0 is the solution0<x<54125 is the solutionx>54125 is not a solution
Solution
x∈(−54125,0)∪(0,54125)
Show Solution
