To solve the equation [tex]\( 2w - 5(w + 1) = 3w + 1 \)[/tex] for [tex]\( w \)[/tex], let's follow the steps systematically:
1. Expand and Simplify the Equation:
[tex]\[
2w - 5(w + 1) = 3w + 1
\][/tex]
First, distribute the [tex]\(-5\)[/tex] on the left side:
[tex]\[
2w - 5w - 5 = 3w + 1
\][/tex]
Simplify the left side by combining like terms:
[tex]\[
-3w - 5 = 3w + 1
\][/tex]
2. Move All Terms Involving [tex]\( w \)[/tex] to One Side:
To isolate the [tex]\( w \)[/tex] terms, add [tex]\( 3w \)[/tex] to both sides:
[tex]\[
-3w + 3w - 5 = 3w + 3w + 1
\][/tex]
Simplify:
[tex]\[
-5 = 6w + 1
\][/tex]
3. Isolate [tex]\( w \)[/tex]:
Subtract 1 from both sides to get the terms involving [tex]\( w \)[/tex] alone:
[tex]\[
-5 - 1 = 6w
\][/tex]
Simplify:
[tex]\[
-6 = 6w
\][/tex]
Divide both sides by 6:
[tex]\[
w = \frac{-6}{6}
\][/tex]
Simplify:
[tex]\[
w = -1
\][/tex]
So, the solution to the equation [tex]\( 2w - 5(w + 1) = 3w + 1 \)[/tex] is:
[tex]\[
w = -1
\][/tex]
Enter the answer in the box:
[tex]\[
w = -1
\][/tex]
