Absolute Value Eqns: solve | 4y - 5 | + 4 = 7y + 8

[Cherry3451]

I am trying to solve the following equation:

|4y-5| + 4 = 7y + 8

I know since it contains an absolue value so it will have 2 answers, but I cannot figure out how to solve it. When I worked it I got the answer -3 and 7/11 but neither of them work once they're plugged in. Can someone please help me!? Thanks so much!

 

[skeeter]

Re: Absolute Value Equalities

|4y-5| + 4 = 7y+8

|4y-5| = 7y+4

at this point, it is important to note that the value of 7y+4 must be greater than or equal to 0 (the absolute value of anything is never negative)

now solve the two cases for absolute value ...

4y - 5 = 7y + 4
y = -3
this solution will not work, why?

4y - 5 = -(7y + 4)
y = 1/11
does this solution work?

 

[Cherry3451]

Re: Absolute Value Equalities

Thanks so much! It makes sense...