[tex] a.\\\dfrac{12}{7}=\dfrac{k}{8}\ \ \ \ |\text{cross multiply}\\\\7k=12\cdot8\\\\7k=96\ \ \ \ |:7\\\\k=\dfrac{96}{7}\to k=13\dfrac{5}{7} [/tex]
[tex] b.\\\dfrac{3}{4}(x+3)=9\ \ \ \ \ |\text{use distributive property}\\\\\dfrac{3}{4}x+\dfrac{3}{4}\cdot3=9\\\\\dfrac{3}{4}x+\dfrac{9}{4}=9\ \ \ \ \ |\cdot4\\\\3x+9=36\ \ \ \ |-9\\\\3x=27\ \ \ \ |:3\\\\x=9 [/tex]
[tex] c.\\\dfrac{4+m}{3}=\dfrac{5}{6}\ \ \ \ \ |\text{cross multiply}\\\\6(4+m)=3\cdot5\ \ \ \ |\text{use distributive property}\\\\6\cdot4+6m=15\\\\24+6m=15\ \ \ \ |-24\\\\6m=-9\ \ \ |:6\\\\m=-\dfrac{9}{6}\\\\m=-\dfrac{3}{2}\\\\m=-1\dfrac{1}{2}\to x=-1.5 [/tex]
[tex] d.\\\dfrac{5}{9}c-\dfrac{3}{4}=\dfrac{7}{9}c\ \ \ \ |+\dfrac{3}{4}\\\\\dfrac{5}{9}c=\dfrac{7}{9}c+\dfrac{3}{4}\ \ \ \ |-\dfrac{7}{9}\\\\-\dfrac{2}{9}c=\dfrac{3}{4}\ \ \ \ |\cdot\left(-\dfrac{9}{2}\right)\\\\c=-\dfrac{27}{8}\to c=-3\dfrac{3}{8} [/tex]
