Solve for a
a=-\frac{3-7x}{x-5}
x\neq 5
Solve for x
x=-\frac{3-5a}{a-7}
a\neq 7
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\left(x-5\right)a=7x-3
Combine all terms containing a.
\frac{\left(x-5\right)a}{x-5}=\frac{7x-3}{x-5}
Divide both sides by x-5.
a=\frac{7x-3}{x-5}
Dividing by x-5 undoes the multiplication by x-5.
ax-5a-7x=-3
Subtract 7x from both sides.
ax-7x=-3+5a
Add 5a to both sides.
\left(a-7\right)x=-3+5a
Combine all terms containing x.
\left(a-7\right)x=5a-3
The equation is in standard form.
\frac{\left(a-7\right)x}{a-7}=\frac{5a-3}{a-7}
Divide both sides by a-7.
x=\frac{5a-3}{a-7}
Dividing by a-7 undoes the multiplication by a-7.
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