How do you solve #abs(4w - 1) = 5w + 37#?

1 Answer
Jul 15, 2015

Answer:

#w=-4#

Explanation:

#abs(4w-1)=5w+37#

Separate the equation into a positive equation and a negative equation.

#4w-1=5w+37# and #-(4w-1)=5w+37#

Positive equation

#4w-1=5w+37#

Add #1# to both sides.

#4w=5w+38#

Subtract #5w# from both sides.

#4w-5w=38#

#-w=38#

Multiply both sides times #-1#.

#w=-38#

Check.

#abs(4*-38-1)=5*-38+37# =

#abs(-152)!=-153#

#152!=-153#

#w!=-38#

Negative equation

#-(4w-1)=5w+37# =

#-4w+1=5w+37#

Subtract #1# from both sides.

#-4w=5w+36#

Subtract #5w# from both sides

#-4w-5w=36#

#-9w=36#

Divide both sides by #-9#.

#w=36/(-9)=-4#

#w=-4#

Check.

#abs(4*-4-1)=5*-4+37# =

#abs(-17)=-20+37# =

#17=17#

#w=-4# checks.