Answer:
x = 7
Step-by-step explanation:
So we have:
[tex]\frac{3}{2}x + \frac{1}{3} = 10\frac{5}{6}[/tex]
In order to make this simpler, we have to make each fraction have a common denominator. Since 2*3=6, let's have 6 be that denominator. Here's what we do for the three fractions:
[tex]\frac{3}{2}*\frac{3}{3} = \frac{9}{6}\\ \frac{1}{3}*\frac{2}{2} = \frac{2}{6}\\\10\frac{5}{6} = \frac{60+5}{6} = \frac{65}{6}[/tex]
Putting those back into our equations, we have:
[tex]\frac{9}{6}x + \frac{2}{6} = \frac{65}{6}[/tex]
We must isolate the x on one side and solve for it by combining like terms:
[tex]\frac{9}{6}x + \frac{2}{6} - \frac{2}{6} = \frac{65}{6} - \frac{2}{6}\\ \frac{9}{6}x = \frac{63}{6}\\\frac{9x}{6}*\frac{6}{9} = \frac{63}{6} * \frac{6}{9}\\\x = 7[/tex]
Our answer is x = 7.
