How do you solve #abs(2x+1)=5#?

Question

Savannah Anderson · Accepted Answer

See a solution process below:

Since the absolute value function takes any term and converts it to a non-negative form, we have to solve the term for both its positive and negative equivalent within the absolute value function. First Solution: #2x + 1 = -5# #2x + 1 - color(red)(1) = -5 - color(red)(1)# #2x + 0 = -6# #2x = -6# #(2x)/color(red)(2) = -6/color(red)(2)# #(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -3# #x = -3# Option 2: #2x + 1 = 5# #2x + 1 - color(red)(1) = 5 - color(red)(1)# #2x + 0 = 4# #2x = 4# #(2x)/color(red)(2) = 4/color(red)(2)# #(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 2# #x = 2# The Solutions Are: #x = -3# and #x = 2#