[tex]\boxed{k=\frac{9}{13}}[/tex]
As I understand, your equation is:
[tex]\frac{5(k+2)-7}{6}=\frac{13-(4-k)}{9}[/tex]
So let's solve this step by step:
Step 1.
[tex]Solving: \\ \\ 5(k+2)-7 \\ \\ By \ Distributive \ Property: \\ \\ 5k+10-7 \\ \\ Simplifying: \\ \\ 5k+3[/tex]
Step 2.
[tex]Solving: \\ \\ 13-(4-k) \\ \\ By \ Distributive \ Property: \\ \\ 13-4+k \\ \\ Simplifying: \\ \\ k+9[/tex]
Step 3.
So we can write our equation in the following form:
[tex]\frac{5k+3}{6}=\frac{k+9}{9}[/tex]
Step 4.
[tex]Multiply \ both \ sides \ by \ 54 \\ \\ \frac{54(5k+3)}{6}=\frac{54(k+9)}{9} \\ \\ 9(5k+3)=6(k+9) \\ \\ Distributive / Property: \\ \\ 45k+27=6k+54 \\ \\ Combine \ like \ terms: \\ \\ 39k=27 \\ \\ Divide\ both \ sides \ by \ 39: \\ \\ k=\frac{27}{39} \\ \\ Simplifying: \\ \\ \boxed{k=\frac{9}{13}}[/tex]
Direct proportion: https://brainly.com/question/13740458#
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