Answer:
w = 3/4 or w = -1/4
Step-by-step explanation:
3l4w - 1l - 5 = 1
Add 5 to both sides.
3|4w - 1| = 6
Divide both sides by 3.
|4w - 1| = 2
Set the inside of the absolute value equal to 2 and -2.
4w - 1 = 2 or 4w - 1 = -2
Add 1 to both sides.
4w = 3 or 4w = -1
Divide both sides by 4.
w = 3/4 or w = -1/4
Check w = 3/4:
3l4w - 1l - 5 = 1
3|4(3/4) - 1| - 5 = 1
3|3 - 1| - 5 = 1
3|2| - 5 = 1
6 - 5 = 1
1 = 1
w = 3/4 works.
Check w = -1/4:
3l4w - 1l - 5 = 1
3|4(-1/4) - 1| - 5 = 1
3|-1 - 1| - 5 = 1
3|-2| - 5 = 1
3(2) - 5 = 1
6 - 5 = 1
1 = 1
w = -1/4 works.
There are no extraneous solutions.
Answer: w = 3/4 or w = -1/4
