How do you solve #abs(n/3)=2#?

Question

Nathan Axel · Accepted Answer

See the entire solution process below:

We must solve the term within the absolute value function for both its negative and positive equivalent because the absolute value function takes any term, whether positive or negative, and converts it to its positive form. First Solution #n/3 = -2# #color(red)(3) xx n/3 = color(red)(3) xx -2# #cancel(color(red)(3)) xx n/color(red)(cancel(color(black)(3))) = -6# #n = -6# Option 2) #n/3 = 2# #color(red)(3) xx n/3 = color(red)(3) xx 2# #cancel(color(red)(3)) xx n/color(red)(cancel(color(black)(3))) = 6# #n = 6# The solution is: #n = -6# and #n = 6#

Ethan Adkins · Answer

undefined To solve the equation $| \frac{n}{3} | = 2$, you need to consider two cases: when $\frac{n}{3}$ is positive and when it is negative.

Case 1: $\frac{n}{3}$ is positive:
1. Set $\frac{n}{3}$ equal to 2: $\frac{n}{3} = 2$.
2. Multiply both sides by 3 to isolate $n$: $n = 6$.

Case 2: $\frac{n}{3}$ is negative:
1. Set $\frac{n}{3}$ equal to -2: $\frac{n}{3} = -2$.
2. Multiply both sides by 3 to isolate $n$: $n = -6$.

So, the solutions to the equation $| \frac{n}{3} | = 2$ are $n = 6$ and $n = -6$.