To solve the equation [tex]\(-47 - 10w = -9w - 40 - 3w\)[/tex], let's go through the steps systematically:
1. Simplify the Right Side:
Combine like terms on the right side of the equation:
[tex]\[
-47 - 10w = -9w - 40 - 3w
\][/tex]
Combine the [tex]\(w\)[/tex] terms:
[tex]\[
-47 - 10w = -12w - 40
\][/tex]
2. Isolate the [tex]\(w\)[/tex] Terms:
Add [tex]\(12w\)[/tex] to both sides of the equation to get all the [tex]\(w\)[/tex] terms on one side:
[tex]\[
-47 - 10w + 12w = -12w + 12w - 40
\][/tex]
Simplify:
[tex]\[
-47 + 2w = -40
\][/tex]
3. Isolate the Constant Term:
Add [tex]\(47\)[/tex] to both sides to isolate the [tex]\(w\)[/tex] term:
[tex]\[
-47 + 2w + 47 = -40 + 47
\][/tex]
Simplify:
[tex]\[
2w = 7
\][/tex]
4. Solve for [tex]\(w\)[/tex]:
Divide both sides by [tex]\(2\)[/tex] to solve for [tex]\(w\)[/tex]:
[tex]\[
w = \frac{7}{2}
\][/tex]
Simplify:
[tex]\[
w = 3.5
\][/tex]
Therefore, the solution to the equation [tex]\(-47 - 10w = -9w - 40 - 3w\)[/tex] is [tex]\(w = 3.5\)[/tex].
