\(a.\)
\(\Leftrightarrow x-5+x-7=-12.\)
\(\Leftrightarrow x=-12+-12\)
\(\Leftrightarrow x=-24\)
\(b.\)
\(\Leftrightarrow3x+2x=-109+44\)
\(\Leftrightarrow5x=-65\)
\(\Rightarrow x=-13\)
\(c.\)
\(\Leftrightarrow2x-10-15+5x=-109\)
\(\Leftrightarrow2x-5x=-109+15+10\)
\(\Leftrightarrow3x=-84\)
\(\Rightarrow x=-28\)
\(d.\)
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d) \(\left(x-3\right)\left(x+5\right)< 0\)
\(\Leftrightarrow\orbr{\begin{cases}x-3< 0\\x+5< 0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x< 3\\x< -5\end{cases}}\)