Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
[tex]\frac{3}{4}x=60\\ \\\frac{3}{4}x*4=60*4\\ \\3x=240\\\\\frac{3x}{3}=\frac{240}{3}\\ \\ x=80[/tex]
Check solution:
[tex]\frac{3}{4}(80)\stackrel{?}{=}60\\\\\frac{3*80}{4}\stackrel{?}{=}60\\\\\frac{240}{4}\stackrel{?}{=}60\\\\60=60[/tex]
Problem 2
[tex]\frac{2}{5}x=42\\ \\\frac{2}{5}x*5=42*5\\ \\2x=210\\\\\frac{2x}{2}=\frac{210}{2}\\ \\ x=105[/tex]
Check solution:
[tex]\frac{2}{5}(105)\stackrel{?}{=}42\\\\\frac{2*105}{5}\stackrel{?}{=}42\\ \\\frac{210}{5}\stackrel{?}{=}42\\ \\42=42[/tex]
Problem 3
[tex]\frac{3}{5}y=40\\ \\\frac{3}{5}y*5=40*5\\ \\3y=200\\\\\frac{3y}{3}=\frac{200}{3}\\ \\ y=\frac{200}{3}[/tex]
Check solution:
[tex]\frac{3}{5}(\frac{200}{3})\stackrel{?}{=} 40\\ \\ \frac{3*200}{5*3}\stackrel{?}{=} 40\\ \\\frac{600}{15}\stackrel{?}{=}40\\\\40=40[/tex]
Problem 4
[tex]-\frac{8}{3}m=6\\\\-\frac{8}{3}m*3=6*3\\ \\-8m=18\\\\\frac{-8m}{-8}=\frac{18}{-8}\\\\m=-\frac{18}{8}\\ \\m=-\frac{9}{4}[/tex]
Check solution:
[tex]-\frac{8}{3}(-\frac{9}{4})\stackrel{?}{=}6\\\\\frac{-8*-9}{3*4}\stackrel{?}{=}6\\\\\frac{72}{12}\stackrel{?}{=}6\\ \\6=6[/tex]
Problem 5
[tex]\frac{5}{6}x=4\\ \\\frac{5}{6}x*6=4*6\\ \\5x=24\\\\\frac{5x}{5}=\frac{24}{5}\\ \\ x=\frac{24}{5}[/tex]
Check solution:
[tex]\frac{5}{6}(\frac{24}{5})\stackrel{?}{=}4\\ \\\frac{5*24}{6*5}\stackrel{?}{=}4\\\\\frac{24}{6}\stackrel{?}{=}4\\ \\4=4[/tex]
Problem 6
[tex]\frac{5}{3}x=12\\ \\\frac{5}{3}x*3=12*3\\ \\5x=36\\\\\frac{5x}{5}=\frac{36}{5}\\ \\x=\frac{36}{5}[/tex]
Check solution:
[tex]\frac{5}{3}(\frac{36}{5})\stackrel{?}{=}12\\\\\frac{5*36}{3*5}\stackrel{?}{=}12\\ \\\frac{36}{3}\stackrel{?}{=}12\\ \\12=12[/tex]
