How do you solve #abs(x/7)-8=-7#?

Question

Eli Assouline · Accepted Answer

See a solution process below:

First, add #color(red)(8)# to each side of the equation to isolate the #x# term while keeping the equation balanced: #abs(x/7) - 8 + color(red)(8) = -7 + color(red)(8)# #abs(x/7) - 0 = 1# #abs(x/7) = 1# 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 #x/7 = -1# #color(red)(7) xx x/7 = color(red)(7) xx -1# #cancel(color(red)(7)) xx x/color(red)(cancel(color(black)(7))) = -7# #x = -7# Option 2) #x/7 = 1# #color(red)(7) xx x/7 = color(red)(7) xx 1# #cancel(color(red)(7)) xx x/color(red)(cancel(color(black)(7))) = 7# #x = 7# The solution is: #x = -7# and #x = 7#

Jameson Allen · Answer

undefined To solve the equation abs(x/7) - 8 = -7, first, add 8 to both sides to isolate the absolute value term. This gives us abs(x/7) = 1. Then, consider the two cases for the absolute value: x/7 = 1 and x/7 = -1. Solve each case separately. For x/7 = 1, multiply both sides by 7 to get x = 7. For x/7 = -1, multiply both sides by 7 to get x = -7. So, the solutions to the equation are x = 7 and x = -7.