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Answer:
x = -5.
Step-by-step explanation:
Solving for x from the equation:
[tex]\frac{2}{3}x - \frac{1}{2} = \frac{1}{3} +\frac{5}{6}x[/tex]
Begin by creating a common denominator for the terms involving x as well as the constants:
[tex]\frac{4}{6}x - \frac{3}{6} = \frac{2}{6} +\frac{5}{6}x[/tex]
Now that each term has a common denominator, we can begin solving for x by isolating the variable:
Subtract 5/6x from both sides:
[tex]\frac{4}{6}x-\frac{5}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]
[tex]-\frac{1}{6}x - \frac{3}{6} = \frac{2}{6}[/tex]
Add 3/6 to both sides:
[tex]-\frac{1}{6}x = \frac{5}{6}[/tex]
Divide -1/6 from both sides. (Multiply by the reciprocal, or -6)
[tex]-\frac{1}{6}x(-6) = \frac{5}{6}(-6)[/tex]
x = -5.
