Solve for b
Solve for x
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bx+\frac{1}{3}=\frac{2}{3}-5x
Swap sides so that all variable terms are on the left hand side.
bx=\frac{2}{3}-5x-\frac{1}{3}
Subtract \frac{1}{3} from both sides.
bx=\frac{1}{3}-5x
Subtract \frac{1}{3} from \frac{2}{3} to get \frac{1}{3}.
xb=\frac{1}{3}-5x
The equation is in standard form.
\frac{xb}{x}=\frac{\frac{1}{3}-5x}{x}
Divide both sides by x.
b=\frac{\frac{1}{3}-5x}{x}
Dividing by x undoes the multiplication by x.
b=-5+\frac{1}{3x}
Divide \frac{1}{3}-5x by x.
\frac{2}{3}-5x-bx=\frac{1}{3}
Subtract bx from both sides.
-5x-bx=\frac{1}{3}-\frac{2}{3}
Subtract \frac{2}{3} from both sides.
-5x-bx=-\frac{1}{3}
Subtract \frac{2}{3} from \frac{1}{3} to get -\frac{1}{3}.
\left(-5-b\right)x=-\frac{1}{3}
Combine all terms containing x.
\left(-b-5\right)x=-\frac{1}{3}
The equation is in standard form.
\frac{\left(-b-5\right)x}{-b-5}=\frac{-\frac{1}{3}}{-b-5}
Divide both sides by -5-b.
x=\frac{-\frac{1}{3}}{-b-5}
Dividing by -5-b undoes the multiplication by -5-b.
x=\frac{1}{3\left(b+5\right)}
Divide -\frac{1}{3} by -5-b.