Certainly! Let's start from the beginning and match Anabel's logic to unravel any misunderstandings and solve the equation step-by-step correctly.
Here's the original equation:
[tex]\[ 2w - 4(w - 3) = -5 \][/tex]
Step 1: Distribute the -4 inside the parentheses
[tex]\[ 2w - 4(w - 3) = 2w - 4w + 12 \][/tex]
Step 2: Simplify the left side by combining like terms
[tex]\[ 2w - 4w + 12 = -2w + 12 \][/tex]
So, now the equation looks like this:
[tex]\[ -2w + 12 = -5 \][/tex]
Step 3: Isolate the [tex]\( w \)[/tex] term
We need to move the constant term [tex]\( 12 \)[/tex] to the right side of the equation:
[tex]\[ -2w + 12 = -5 \][/tex]
Subtract [tex]\( 12 \)[/tex] from both sides:
[tex]\[ -2w = -5 - 12 \][/tex]
[tex]\[ -2w = -17 \][/tex]
Step 4: Solve for [tex]\( w \)[/tex]
Divide both sides of the equation by [tex]\( -2 \)[/tex]:
[tex]\[ w = \frac{-17}{-2} \][/tex]
[tex]\[ w = 8.5 \][/tex]
So, the solution to the equation is:
[tex]\[ w = 8.5 \][/tex]
