Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for n
n≥−135514098
Alternative Form
n∈[−135514098,+∞)
Evaluate
−13n4×n≤18
Multiply
More Steps

Evaluate
−13n4×n
Multiply the terms with the same base by adding their exponents
−13n4+1
Add the numbers
−13n5
−13n5≤18
Move the expression to the left side
−13n5−18≤0
Rewrite the expression
−13n5−18=0
Move the constant to the right-hand side and change its sign
−13n5=0+18
Removing 0 doesn't change the value,so remove it from the expression
−13n5=18
Change the signs on both sides of the equation
13n5=−18
Divide both sides
1313n5=13−18
Divide the numbers
n5=13−18
Use b−a=−ba=−ba to rewrite the fraction
n5=−1318
Take the 5-th root on both sides of the equation
5n5=5−1318
Calculate
n=5−1318
Simplify the root
More Steps

Evaluate
5−1318
An odd root of a negative radicand is always a negative
−51318
To take a root of a fraction,take the root of the numerator and denominator separately
−513518
Multiply by the Conjugate
513×5134−518×5134
Simplify
513×5134−518×528561
Multiply the numbers
More Steps

Evaluate
−518×528561
The product of roots with the same index is equal to the root of the product
−518×28561
Calculate the product
−5514098
513×5134−5514098
Multiply the numbers
More Steps

Evaluate
513×5134
The product of roots with the same index is equal to the root of the product
513×134
Calculate the product
5135
Reduce the index of the radical and exponent with 5
13
13−5514098
Calculate
−135514098
n=−135514098
Determine the test intervals using the critical values
n<−135514098n>−135514098
Choose a value form each interval
n1=−2n2=0
To determine if n<−135514098 is the solution to the inequality,test if the chosen value n=−2 satisfies the initial inequality
More Steps

Evaluate
−13(−2)5≤18
Multiply the terms
More Steps

Evaluate
−13(−2)5
Evaluate the power
−13(−32)
Multiply the numbers
416
416≤18
Check the inequality
false
n<−135514098 is not a solutionn2=0
To determine if n>−135514098 is the solution to the inequality,test if the chosen value n=0 satisfies the initial inequality
More Steps

Evaluate
−13×05≤18
Simplify
More Steps

Evaluate
−13×05
Calculate
−13×0
Any expression multiplied by 0 equals 0
0
0≤18
Check the inequality
true
n<−135514098 is not a solutionn>−135514098 is the solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
n≥−135514098 is the solution
Solution
n≥−135514098
Alternative Form
n∈[−135514098,+∞)
Show Solution
