#color(red)(w = 5/7)# and #color(red)(w = 5)# are solutions.

There are #color(red)("no")# extraneous solutions.

**SOLVE**

#|5-4w| = 3w#

We need to write two different equations without the absolute value symbols and solve for #w#.

These equations are:

**(1): **#(5-4w) = 3w#

**(2): **#-(5-4w) = 2w#

**Solve Equation 1:**

#5-4w = 3w#

Add #4w# to each side.

#5 = 7w#

Divide each side by #7#.

#w = 5/7#

**Solve Equation 2:**

#−(5-4w) = 3w#

Remove parentheses.

#-5+4w= 3w#

Subtract #3w# from each side.

#-5+w = 0#

Add #5# to each side..

#w = 5#

The solutions are #w = 5/7# and #w = 5#.

**CHECK FOR EXTRANEOUS SOLUTIONS:**

If #w=5/7#,

#|5-4w|=3w#

#|5-4(5/7)|= 3(5/7)#

#|5-20/7| = 15/7#

#|(35-20)/7| =15/7#

#|15/7| = 15/7#

#15/7=15/7#

#w = 5/7# is a solution.

If #w=5#,

#|5-4w| = 3w#

#|5-4(5)| = 3(5)#

#|5-20| = 15#

#|15| = 15#

#15 = 15#

#w=5# is a solution.

There are no extraneous solutions.