To solve the equation [tex]\(-4w + 5 = 3w - 58\)[/tex], let's go through the steps one by one.
1. Start with the given equation:
[tex]\[
-4w + 5 = 3w - 58
\][/tex]
2. Combine all the [tex]\(w\)[/tex] terms on one side of the equation. We'll do this by adding [tex]\(4w\)[/tex] to both sides:
[tex]\[
-4w + 4w + 5 = 3w + 4w - 58
\][/tex]
Which simplifies to:
[tex]\[
5 = 7w - 58
\][/tex]
3. Next, combine all constant terms on the other side of the equation. We'll do this by adding [tex]\(58\)[/tex] to both sides:
[tex]\[
5 + 58 = 7w - 58 + 58
\][/tex]
Which simplifies to:
[tex]\[
63 = 7w
\][/tex]
4. Finally, solve for [tex]\(w\)[/tex] by dividing both sides by [tex]\(7\)[/tex]:
[tex]\[
\frac{63}{7} = \frac{7w}{7}
\][/tex]
Which simplifies to:
[tex]\[
9 = w
\][/tex]
So, the solution to the equation [tex]\(-4w + 5 = 3w - 58\)[/tex] is:
[tex]\[
w = 9
\][/tex]
