How do you solve #abs(-9+v)/8=3#?

Question

Hazel Anglin · Accepted Answer

See a solution process below:

First, multiply each side of the equation by #color(red)(8)# to isolate the absolute value function while keeping the equation balanced: #color(red)(8) xx abs(-9 + v)/8 = color(red)(8) xx 3# #cancel(color(red)(8)) xx abs(-9 + v)/color(red)(cancel(color(black)(8))) = 24# #abs(-9 + v) = 24# 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 non-negative form. First Solution: #-9 + v = -24# #color(red)(9) - 9 + v = color(red)(9) - 24# #0 + v = -15# #v = -15# Option 2: #-9 + v = 24# #color(red)(9) - 9 + v = color(red)(9) + 24# #0 + v = 33# #v = 33# The Solutions Are: #v = -15# and #v = 33#

Eva Adamson · Answer

undefined To solve the equation abs(-9+v)/8 = 3:

1. Multiply both sides of the equation by 8 to eliminate the fraction: abs(-9+v) = 24
2. Remove the absolute value by considering both the positive and negative cases: 
   - For the positive case: -9 + v = 24
   - For the negative case: -(-9 + v) = 24
3. Solve each case separately:
   - For the positive case: v = 24 + 9 = 33
   - For the negative case: -(-9 + v) = 24
     => 9 - v = 24
     => -v = 24 - 9
     => -v = 15
     => v = -15

So, the solutions for v are v = 33 and v = -15.