How do you solve #8abs(3-3n)-5=91#?

Question

Avery Alexander · Accepted Answer

First, isolate the absolute value.

#8|3 - 3n| - 5 = 91#

#8|3 - 3n| = 96#

#|3 - 3n| = 12#

We must now consider the negative case and the positive case.

Case 1: The absolute value is positive

#3 - 3n = 12#

#-3n = 9#

#n = -3#

Case 2: The absolute value is negative

#-(3 - 3n) = 12#

#-3 + 3n = 12#

#3n = 15#

#n = 5#

Hence, the solution set is #{-3, 5}#.

Hopefully this helps!

Savannah Anderson · Answer

undefined To solve the equation $8|3-3n|-5=91$, first, add 5 to both sides to isolate the absolute value term, resulting in $8|3-3n|=96$. Then, divide both sides by 8 to isolate the absolute value term, yielding $|3-3n|=12$. Now, you have two cases to consider:

1. When $3-3n$ is positive, you have $3-3n=12$. 
2. When $3-3n$ is negative, you have $3-3n=-12$.

Solve each case separately for $n$.

1. For $3-3n=12$, solve for $n$ to get $n=-3$.
2. For $3-3n=-12$, solve for $n$ to get $n=5$.

Therefore, the solutions to the equation are $n=-3$ and $n=5$.