How do you solve #|5a + 5| = | 6a - 3|#?

1 Answer
MathFact-orials.blogspot.com
Mar 12, 2017

#a=8,-2/11#

Explanation:

When working a problem like this, the first question I always find myself asking is "How many solutions am I looking for?" To answer that, I took a minute to graph the equation and it turns out there are 2 (I've magnified on each solution):

graph{(y-abs(5x+5))(y-abs(6x-3))=0 [-4, 5, -2, 7.34]}

graph{(y-abs(5x+5))(y-abs(6x-3))=0 [7, 9, 35, 50]}

Ok - so how do we find them algebraically? By looking at the positive and negative values arising from the absolute value signs. We only need set one side for #pm# as that will satisfy (I'll do all the conditions to demonstrate):

Both Positive

#abs(5a+5)=abs(6a-3)#

#5a+5=6a-3#

#a=8#

Negative Left

#-(5a+5)=6a-3#

#-5a-5=6a-3#

#11a=-2#

#a=-2/11#

Negative Right

#5a+5=-(6a-3)#

#5a+5=-6a+3#

#11a=-2#

#a=-2/11#

Both Negative

#abs(5a+5)=abs(6a-3)#

#-(5a+5)=-(6a-3)#

#-5a-5=-6a+3#

#a=8#

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