How do you solve #abs(y+3)+4=20#?

Question

Julia Adams · Accepted Answer

#y=-19" or " y=13#

#"Isolate " |y+3|" by subtracting 4 from both sides"#

#|y+3|cancel(+4)cancel(-4)=20-4#

#rArr|y+3|=16#

#"the expression inside the absolute value can be positive or"# #"negative"#

#rArry+3=16toy=16-3=13larr(color(red)(1))" or "#

#-(y+3)=16#

#rArr-y-3=16to-y=16+3toy=-19larr(color(red)(2))#

#color(blue)"As a check"#

These values are the solutions if you substitute them into the left side of the equation and see if they equal the right side.

#y=13to|13+3|+4=|16|+4=16+4=20#

#y=-19to|-19+3|+4=|-16|+4=20#

#rArry=-19" or " y=13" are the solutions"#

Nathan Axel · Answer

undefined To solve the equation abs(y+3) + 4 = 20, first isolate the absolute value term:

abs(y+3) = 20 - 4
abs(y+3) = 16

Now, split the equation into two cases based on the possible values of (y+3):

Case 1: y+3 is positive or zero:
For this case, abs(y+3) = y+3. So, we have:
y + 3 = 16

Case 2: y+3 is negative:
For this case, abs(y+3) = -(y+3). So, we have:
-(y + 3) = 16

Now, solve each case separately:

Case 1:
y + 3 = 16
y = 16 - 3
y = 13

Case 2:
-(y + 3) = 16
-y - 3 = 16
-y = 16 + 3
-y = 19
Multiply both sides by -1 to solve for y:
y = -19

So, the solutions are y = 13 and y = -19.