# How do you graph and solve #|3y+2|=|2y-5|#?

##### 2 Answers

#### Explanation:

or

(i)

(ii)

#### Explanation:

Find the points when the term inside the absolute value switches sign.

#3y+2=0#

#y=-2/3#

#3y+2<0# when#y<-2/3# ,#>0# when#y> -2/3#

#2y-5=0#

#y=5/2#

#2y-5<0# when#y<5/2# ,#>0# when#y>5/2#

From this, we have three distinct ranges of numbers:

In this set, both of the terms inside the absolute value functions will be negative. Take the negative versions of each of the absolute value expressions.

#-(3y+2)=-(2y-5)#

Solve. The answer is only valid if

#3y+2=2y-5#

#y=-7#

This is a valid answer.

Here, the

#3y+2=-(2y-5)#

#3y+2=-2y+5#

#y=3/5#

This is also a valid answer, since

From the first set, we know this will result in an answer of

Thus,

graph{abs(3x+2)-abs(2x-5) [-19.8, 20.75, -8.48, 11.79]}