How do you solve #abs(-2n+6)=6#?

Question

Hazel Anglin · Accepted Answer

Because this problem contains an absolute value we need to handle it differently than a regular equation. See full explanation below.

We must approach this problem differently than we would a regular equation because it involves an absolute value. Since the absolute value function converts any term, whether positive or negative, into its positive equivalent, we must solve the term inside the absolute value for both the equation's positive and negative solutions. First Solution #-2n + 6 = 6# #-2n + 6 - color(red)(6) = 6 - color(red)(6)# #-2n + 0 = 0# #-2n = 0# #(-2n)/color(red)(-2) = 0/color(red)(-2)# #(color(red)(cancel(color(black)(-2)))n)/cancel(color(red)(-2)) = 0# #n = 0# Option 2) #-2n + 6 = -6# #-2n + 6 - color(red)(6) = -6 - color(red)(6)# #-2n + 0 = -12# #-2n = -12# #(-2n)/color(red)(-2) = -12/color(red)(-2)# #(color(red)(cancel(color(black)(-2)))n)/cancel(color(red)(-2)) = 6# #n = 6#

Eva Adamson · Answer

undefined To solve the equation abs(-2n + 6) = 6:

1. Break the equation into two separate equations: -2n + 6 = 6 and -2n + 6 = -6.
2. Solve each equation individually:
   - For -2n + 6 = 6, subtract 6 from both sides to get -2n = 0, then divide by -2 to find n = 0.
   - For -2n + 6 = -6, subtract 6 from both sides to get -2n = -12, then divide by -2 to find n = 6.
3. Combine the solutions: n = {0, 6}.