How do you solve #3/4abs(y+2)=6#?

2 Answers
Mar 26, 2018

Answer:

See a solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(4)/color(blue)(3)# to isolate the absolute value function while keeping the equation balanced:

#color(red)(4)/color(blue)(3) xx 3/4abs(y + 2) = color(red)(4)/color(blue)(3) xx 6#

#12/12abs(y + 2) = 24/color(blue)(3)#

#1abs(y + 2) = 8#

#abs(y + 2) = 8#

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

#y + 2 = -8#

#y + 2 - color(red)(2) = -8 - color(red)(2)#

#y + 0 = -10#

#y = -10#

Solution 2:

#y + 2 = 8#

#y + 2 - color(red)(2) = 8 - color(red)(2)#

#y + 0 = 6#

#y = 6#

The Solution Set Is:

#x = {-10, 6}#

Mar 26, 2018

Answer:

#y= -10, 6#

Explanation:

Because you don't know if y is positive or negative, #|y+2|# equals both #(y+2)# and #-(y+2)#

Start by dividing both sides by #3/4#:

#|y+2|=6(4/3)#

#|y+2|=8#

Then set up two equations and solve:

#y+2=8#

#y=6#

and

#-(y+2)=8#

#-y-2=8#

#-y=10#

Multiply both sides by #-1#

#-y xx -1 = 10 xx -1#

#y = -10#