Answer :

The equation is the following:

[tex]\frac{1}{2}k-(k+\frac{1}{5})=\frac{1}{10}(k+2)[/tex]

First let's eliminate the denominators. We can do that by multiplying both sides of the equation by 10:

[tex]\begin{gathered} \frac{10}{2}k-10(k+\frac{1}{5})=k+2 \\ 5k-10k-2=k+2 \end{gathered}[/tex]

Then, we isolate the terms with the variable in one side of the equation, and the terms without the variable in the other side:

[tex]\begin{gathered} 5k-10k-k=2+2 \\ -6k=4 \end{gathered}[/tex]

Finally, we divide both sides by the number multiplying the variable:

[tex]\begin{gathered} \frac{-6k}{-6}=\frac{4}{-6} \\ k-\frac{-4}{6}=-\frac{2}{3} \end{gathered}[/tex]

So the value of k is -2/3

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