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Solve for x (complex solution)
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\frac{5}{12}x+\frac{1}{5}+3=\frac{5}{12}x+\frac{16}{5}
Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.
\frac{5}{12}x+\frac{1}{5}+\frac{15}{5}=\frac{5}{12}x+\frac{16}{5}
Convert 3 to fraction \frac{15}{5}.
\frac{5}{12}x+\frac{1+15}{5}=\frac{5}{12}x+\frac{16}{5}
Since \frac{1}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.
\frac{5}{12}x+\frac{16}{5}=\frac{5}{12}x+\frac{16}{5}
Add 1 and 15 to get 16.
\frac{5}{12}x+\frac{16}{5}-\frac{5}{12}x=\frac{16}{5}
Subtract \frac{5}{12}x from both sides.
\frac{16}{5}=\frac{16}{5}
Combine \frac{5}{12}x and -\frac{5}{12}x to get 0.
\text{true}
Compare \frac{16}{5} and \frac{16}{5}.
x\in \mathrm{C}
This is true for any x.
\frac{5}{12}x+\frac{1}{5}+3=\frac{5}{12}x+\frac{16}{5}
Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.
\frac{5}{12}x+\frac{1}{5}+\frac{15}{5}=\frac{5}{12}x+\frac{16}{5}
Convert 3 to fraction \frac{15}{5}.
\frac{5}{12}x+\frac{1+15}{5}=\frac{5}{12}x+\frac{16}{5}
Since \frac{1}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.
\frac{5}{12}x+\frac{16}{5}=\frac{5}{12}x+\frac{16}{5}
Add 1 and 15 to get 16.
\frac{5}{12}x+\frac{16}{5}-\frac{5}{12}x=\frac{16}{5}
Subtract \frac{5}{12}x from both sides.
\frac{16}{5}=\frac{16}{5}
Combine \frac{5}{12}x and -\frac{5}{12}x to get 0.
\text{true}
Compare \frac{16}{5} and \frac{16}{5}.
x\in \mathrm{R}
This is true for any x.