To solve for [tex]\( w \)[/tex] in the equation [tex]\(\frac{8}{w+5} = \frac{9}{w+6}\)[/tex], we need to follow these steps:
1. Cross-Multiply:
Cross-multiplying the fractions gives:
[tex]\[
8(w + 6) = 9(w + 5)
\][/tex]
2. Distribute and Simplify:
Distribute the constants on both sides of the equation:
[tex]\[
8w + 48 = 9w + 45
\][/tex]
3. Isolate the Variable:
To isolate [tex]\( w \)[/tex], we need to collect all terms involving [tex]\( w \)[/tex] on one side of the equation and constants on the other side. Subtract [tex]\( 8w \)[/tex] from both sides:
[tex]\[
48 = 9w + 45 - 8w
\][/tex]
[tex]\[
48 = w + 45
\][/tex]
4. Solve for [tex]\( w \)[/tex]:
Subtract 45 from both sides to isolate [tex]\( w \)[/tex]:
[tex]\[
48 - 45 = w
\][/tex]
[tex]\[
3 = w
\][/tex]
Thus, the solution for [tex]\( w \)[/tex] is:
[tex]\[
w = 3
\][/tex]
