How do you solve # 6|y+1|=60#?

Question

Abigail Allen · Accepted Answer

See the entire solution process below.

First, divide each side of the equation by #color(red)(6)# to isolate the absolute value term: #(6abs(y + 1))/color(red)(6) = 60/color(red)(6)# #(color(red)(cancel(color(black)(6)))abs(y + 1))/cancel(color(red)(6)) = 10# #abs(y + 1) = 10# You must solve the term within the absolute value function for both the negative and positive form of what it is equated to in order to solve this because the absolute value function converts any term, whether positive or negative, into its positive form. First Solution #y + 1 = -10# #y + 1 - color(red)(1) = -10 - color(red)(1)# #y + 0 = -11# #y = -11# Option 2) #y + 1 = 10# #y + 1 - color(red)(1) = 10 - color(red)(1)# #y + 0 = 9# #y = 9# The solution is #y = -11# and #y = 9#

Eva Adamson · Answer

undefined To solve the equation $ 6|y+1| = 60 $, you first isolate the absolute value term by dividing both sides of the equation by 6. This gives you $ |y+1| = 10 $. Then, you split the equation into two cases: $ y+1 = 10 $ and $ y+1 = -10 $. Solve each case separately to find the possible values of $ y $. For the first case, subtract 1 from both sides to get $ y = 9 $. For the second case, subtract 1 from both sides to get $ y = -11 $. Therefore, the solutions to the equation are $ y = 9 $ and $ y = -11 $.