cheap answer, multiply both sides by the LCD, in this case 2, that way, you get rid of the denominators.
[tex]\bf 5x-\cfrac{1}{2}(3x+8)=-4-\cfrac{7}{2}x\impliedby \times \stackrel{LCD}{2}
\\\\\\
\boxed{2}\cdot 5x-\boxed{2}\cdot \cfrac{1}{2}(3x+8)=-\boxed{2}\cdot 4-\boxed{2}\cdot \cfrac{7}{2}x
\\\\\\
10x-(3x+8)=-8-7x\implies 10x-3x-8=-8-7x
\\\\\\
7x-8=-8-7x\implies 14x=-8+8\implies 14x=0
\\\\\\
x=\cfrac{0}{14}\implies x=0[/tex]
