Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
x∈(−∞,−7684035)∪(7684035,+∞)
Evaluate
7x6>5
Move the expression to the left side
7x6−5>0
Rewrite the expression
7x6−5=0
Move the constant to the right-hand side and change its sign
7x6=0+5
Removing 0 doesn't change the value,so remove it from the expression
7x6=5
Divide both sides
77x6=75
Divide the numbers
x6=75
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±675
Simplify the expression
More Steps

Evaluate
675
To take a root of a fraction,take the root of the numerator and denominator separately
6765
Multiply by the Conjugate
67×67565×675
Simplify
67×67565×616807
Multiply the numbers
More Steps

Evaluate
65×616807
The product of roots with the same index is equal to the root of the product
65×16807
Calculate the product
684035
67×675684035
Multiply the numbers
More Steps

Evaluate
67×675
The product of roots with the same index is equal to the root of the product
67×75
Calculate the product
676
Reduce the index of the radical and exponent with 6
7
7684035
x=±7684035
Separate the equation into 2 possible cases
x=7684035x=−7684035
Determine the test intervals using the critical values
x<−7684035−7684035<x<7684035x>7684035
Choose a value form each interval
x1=−2x2=0x3=2
To determine if x<−7684035 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps

Evaluate
7(−2)6>5
Multiply the terms
More Steps

Evaluate
7(−2)6
Evaluate the power
7×64
Multiply the numbers
448
448>5
Check the inequality
true
x<−7684035 is the solutionx2=0x3=2
To determine if −7684035<x<7684035 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps

Evaluate
7×06>5
Simplify
More Steps

Evaluate
7×06
Calculate
7×0
Any expression multiplied by 0 equals 0
0
0>5
Check the inequality
false
x<−7684035 is the solution−7684035<x<7684035 is not a solutionx3=2
To determine if x>7684035 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps

Evaluate
7×26>5
Multiply the terms
More Steps

Evaluate
7×26
Evaluate the power
7×64
Multiply the numbers
448
448>5
Check the inequality
true
x<−7684035 is the solution−7684035<x<7684035 is not a solutionx>7684035 is the solution
Solution
x∈(−∞,−7684035)∪(7684035,+∞)
Show Solution
