Question

if ( x = 3(y + w) - 1 ), what is the value of ( w ) in terms of ( x ) and ( y )?

( circ ) ( w = \frac{x - 3y}{3} )
( circ ) ( w = \frac{x - 3y + 1}{3} )
( circ ) ( w = x - 3y + 1 )
( circ ) ( w = \frac{x + 1}{3y} )

Explanation:

Step1: Start with the given equation

We have the equation \( x = 3(y + w)-1 \). Our goal is to solve for \( w \) in terms of \( x \) and \( y \).

Step2: Expand the right - hand side

Using the distributive property \( a(b + c)=ab+ac \), where \( a = 3 \), \( b=y \) and \( c = w \), we get \( x=3y + 3w-1 \).

Step3: Isolate the term with \( w \)

First, we add 1 to both sides of the equation to get \( x + 1=3y+3w \). Then, we subtract \( 3y \) from both sides: \( x + 1-3y=3w \).

Step4: Solve for \( w \)

Divide both sides of the equation \( x-3y + 1=3w \) by 3. We have \( w=\frac{x - 3y+1}{3} \).

Answer:

\( w=\frac{x - 3y + 1}{3} \) (corresponding to the second option)