Solve for k
k=\frac{x}{2}+\frac{1}{3}
Solve for x
x=2k-\frac{2}{3}
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3\pi x+2\pi =6k\pi
Multiply both sides of the equation by 6, the least common multiple of 2,3.
6k\pi =3\pi x+2\pi
Swap sides so that all variable terms are on the left hand side.
6\pi k=3\pi x+2\pi
The equation is in standard form.
\frac{6\pi k}{6\pi }=\frac{\pi \left(3x+2\right)}{6\pi }
Divide both sides by 6\pi .
k=\frac{\pi \left(3x+2\right)}{6\pi }
Dividing by 6\pi undoes the multiplication by 6\pi .
k=\frac{x}{2}+\frac{1}{3}
Divide \pi \left(2+3x\right) by 6\pi .
3\pi x+2\pi =6k\pi
Multiply both sides of the equation by 6, the least common multiple of 2,3.
3\pi x=6k\pi -2\pi
Subtract 2\pi from both sides.
3\pi x=6\pi k-2\pi
The equation is in standard form.
\frac{3\pi x}{3\pi }=\frac{6\pi k-2\pi }{3\pi }
Divide both sides by 3\pi .
x=\frac{6\pi k-2\pi }{3\pi }
Dividing by 3\pi undoes the multiplication by 3\pi .
x=2k-\frac{2}{3}
Divide -2\pi +6\pi k by 3\pi .
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