To solve the given equation, we first apply the distributive property on the left side.
So, we have:
[tex]\begin{gathered} 14(0.5+k)=-14 \\ 14\cdot0.5+14\cdot k=-14 \\ 7+14k=-14 \\ \text{ Subtract 7 from both sides of the equation} \\ 7-7+14k=-14-7 \\ 14k=-21 \\ \text{ Divide by 14 from both sides} \\ \frac{14k}{14}=-\frac{21}{14} \\ k=-\frac{21}{14} \end{gathered}[/tex]Finally, we simplify.
[tex]\begin{gathered} k=-\frac{3\cdot7}{2\cdot7} \\ $\boldsymbol{k=-\frac{3}{2}}$ \end{gathered}[/tex]Therefore, the solution of the given equation is -3/2.
