How do you solve #abs(4y+5)=7#?

1 Answer
smendyka
Dec 21, 2016

#y = 1/2# and #y = -3#

Explanation:

Because the absolute value function transform positive or negative number into a positive number we need to solve the interior of the absolute value function for both the negative and positive form of its equality:

Solution 1)

#4y + 5 = color(blue)(7)#

#4y + 5 - color(red)(5) = 7 - color(red)(5)#

#4y + 0 = 2#

#4y = 2#

#(4y)/color(red)(4) = 2/color(red)(4)#

#(color(red)(cancel(color(black)(4)))y)/color(red)(cancel(color(black)(4))) = 1/2#

#y = 1/2#

Solution 2)

#4y + 5 = color(blue)(-7)#

#4y + 5 - color(red)(5) = -7 - color(red)(5)#

#4y + 0 = -12#

#4y = -12#

#(4y)/color(red)(4) = -12/color(red)(4)#

#(color(red)(cancel(color(black)(4)))y)/color(red)(cancel(color(black)(4))) = -3#

#y = -3#

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