7. $\frac{8}{m - 9}=\frac{6}{m - 8}$

Explanation:

Step1: Cross - multiply

$8(m - 8)=6(m - 9)$

Step2: Expand both sides

$8m-64 = 6m-54$

Step3: Move terms with $m$ to one side

$8m - 6m=-54 + 64$

Step4: Simplify

$2m = 10$

Step5: Solve for $m$

$m = 5$

Answer:

$m = 5$