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

1 Answer
Jul 15, 2015

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.