Certainly! Let's solve the equation step-by-step.
First, distribute the 9 on the left side of the equation:
[tex]\[ 9(w - 4) = 9w - 36 \][/tex]
Next, distribute the 5 on the right side of the equation:
[tex]\[ 5(3w - 2) = 15w - 10 \][/tex]
Now substitute the distributed expressions back into the equation:
[tex]\[ 9w - 36 - 7w = 15w - 10 \][/tex]
Combine like terms on the left side of the equation:
[tex]\[ (9w - 7w) - 36 = 15w - 10 \][/tex]
[tex]\[ 2w - 36 = 15w - 10 \][/tex]
To isolate the variable [tex]\( w \)[/tex], move all terms containing [tex]\( w \)[/tex] to one side of the equation and the constant terms to the other:
[tex]\[ 2w - 15w = -10 + 36 \][/tex]
[tex]\[ -13w = 26 \][/tex]
Now, divide both sides by [tex]\(-13\)[/tex] to solve for [tex]\( w \)[/tex]:
[tex]\[ w = \frac{26}{-13} \][/tex]
[tex]\[ w = -2 \][/tex]
Thus, the solution to the equation [tex]\( 9(w-4) - 7w = 5(3w-2) \)[/tex] is [tex]\(\boxed{-2}\)[/tex].
