Let's solve the equation step-by-step:
Given the equation:
[tex]\[ 9(w - 4) - 7w = 5(3w - 2) \][/tex]
1. Distribute the constants inside the parentheses:
[tex]\[ 9(w - 4) = 9w - 36 \][/tex]
[tex]\[ 5(3w - 2) = 15w - 10 \][/tex]
Now the equation looks like:
[tex]\[ 9w - 36 - 7w = 15w - 10 \][/tex]
2. Combine like terms on the left side of the equation:
[tex]\[ (9w - 7w) - 36 = 15w - 10 \][/tex]
[tex]\[ 2w - 36 = 15w - 10 \][/tex]
3. Move all terms involving [tex]\( w \)[/tex] to one side and constant terms to the other side of the equation:
[tex]\[ 2w - 15w = 36 - 10 \][/tex]
[tex]\[ -13w = 26 \][/tex]
4. Solve for [tex]\( w \)[/tex] by isolating the variable:
[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]\[ w = -2 \][/tex]
So out of the given options:
- [tex]\( w = -\frac{34}{13} \)[/tex]
- [tex]\( w = -2 \)[/tex]
- [tex]\( w = \frac{6}{13} \)[/tex]
- [tex]\( w = 26 \)[/tex]
The correct answer is:
[tex]\[ w = -2 \][/tex]
