Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for z
z<−1
Alternative Form
z∈(−∞,−1)
Evaluate
5z5<−5
Move the expression to the left side
5z5−(−5)<0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
5z5+5<0
Rewrite the expression
5z5+5=0
Move the constant to the right-hand side and change its sign
5z5=0−5
Removing 0 doesn't change the value,so remove it from the expression
5z5=−5
Divide both sides
55z5=5−5
Divide the numbers
z5=5−5
Divide the numbers
More Steps

Evaluate
5−5
Reduce the numbers
1−1
Calculate
−1
z5=−1
Take the 5-th root on both sides of the equation
5z5=5−1
Calculate
z=5−1
Simplify the root
More Steps

Evaluate
5−1
An odd root of a negative radicand is always a negative
−51
Simplify the radical expression
−1
z=−1
Determine the test intervals using the critical values
z<−1z>−1
Choose a value form each interval
z1=−2z2=0
To determine if z<−1 is the solution to the inequality,test if the chosen value z=−2 satisfies the initial inequality
More Steps

Evaluate
5(−2)5<−5
Multiply the terms
More Steps

Evaluate
5(−2)5
Evaluate the power
5(−32)
Multiply the numbers
−160
−160<−5
Check the inequality
true
z<−1 is the solutionz2=0
To determine if z>−1 is the solution to the inequality,test if the chosen value z=0 satisfies the initial inequality
More Steps

Evaluate
5×05<−5
Simplify
More Steps

Evaluate
5×05
Calculate
5×0
Any expression multiplied by 0 equals 0
0
0<−5
Check the inequality
false
z<−1 is the solutionz>−1 is not a solution
Solution
z<−1
Alternative Form
z∈(−∞,−1)
Show Solution
