Solve for a
a=b+4-\frac{7}{x}
x\neq 0
Solve for b
b=a-4+\frac{7}{x}
x\neq 0
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ax=4x+bx-7
Subtract 7 from both sides.
xa=bx+4x-7
The equation is in standard form.
\frac{xa}{x}=\frac{bx+4x-7}{x}
Divide both sides by x.
a=\frac{bx+4x-7}{x}
Dividing by x undoes the multiplication by x.
a=b+4-\frac{7}{x}
Divide 4x+bx-7 by x.
4x+bx=ax+7
Swap sides so that all variable terms are on the left hand side.
bx=ax+7-4x
Subtract 4x from both sides.
xb=ax-4x+7
The equation is in standard form.
\frac{xb}{x}=\frac{ax-4x+7}{x}
Divide both sides by x.
b=\frac{ax-4x+7}{x}
Dividing by x undoes the multiplication by x.
b=a-4+\frac{7}{x}
Divide ax+7-4x by x.
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