[tex]f(x)=(-4m+1)x-3\frac{1}{2}m+4[/tex]
a)
[tex]f(8)=0\\(-4m+1)*8-3\frac{1}{2}m+4=0\\-32m+8-3\frac{1}{2}m+4=0\\-35\frac{1}{2}m+12=0\\-35\frac{1}{2}m=-12\ |:-35\frac{1}{2}\\m=-12:(-\frac{71}{2})\\m=12*\frac{2}{71}\\m=\frac{24}{71}[/tex]
b)
[tex]-4m+1 > 0\\-4m > -1\ |:(-4)\\m < \frac{1}{4}\\m\in(-\infty,\frac{1}{4})[/tex]