Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{2\left(1+2b-2x\right)}{3\left(x-5\right)}\text{, }&x\neq 5\\a\in \mathrm{C}\text{, }&x=5\text{ and }b=\frac{9}{2}\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{2\left(1+2b-2x\right)}{3\left(x-5\right)}\text{, }&x\neq 5\\a\in \mathrm{R}\text{, }&x=5\text{ and }b=\frac{9}{2}\end{matrix}\right.
Solve for b
b=-\frac{3ax}{4}+\frac{15a}{4}+x-\frac{1}{2}
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4x-2=4b+3ax-15a
Use the distributive property to multiply 3 by ax-5a.
4b+3ax-15a=4x-2
Swap sides so that all variable terms are on the left hand side.
3ax-15a=4x-2-4b
Subtract 4b from both sides.
\left(3x-15\right)a=4x-2-4b
Combine all terms containing a.
\left(3x-15\right)a=4x-4b-2
The equation is in standard form.
\frac{\left(3x-15\right)a}{3x-15}=\frac{4x-4b-2}{3x-15}
Divide both sides by 3x-15.
a=\frac{4x-4b-2}{3x-15}
Dividing by 3x-15 undoes the multiplication by 3x-15.
a=\frac{2\left(2x-2b-1\right)}{3\left(x-5\right)}
Divide 4x-2-4b by 3x-15.
4x-2=4b+3ax-15a
Use the distributive property to multiply 3 by ax-5a.
4b+3ax-15a=4x-2
Swap sides so that all variable terms are on the left hand side.
3ax-15a=4x-2-4b
Subtract 4b from both sides.
\left(3x-15\right)a=4x-2-4b
Combine all terms containing a.
\left(3x-15\right)a=4x-4b-2
The equation is in standard form.
\frac{\left(3x-15\right)a}{3x-15}=\frac{4x-4b-2}{3x-15}
Divide both sides by 3x-15.
a=\frac{4x-4b-2}{3x-15}
Dividing by 3x-15 undoes the multiplication by 3x-15.
a=\frac{2\left(2x-2b-1\right)}{3\left(x-5\right)}
Divide 4x-2-4b by 3x-15.
4x-2=4b+3ax-15a
Use the distributive property to multiply 3 by ax-5a.
4b+3ax-15a=4x-2
Swap sides so that all variable terms are on the left hand side.
4b-15a=4x-2-3ax
Subtract 3ax from both sides.
4b=4x-2-3ax+15a
Add 15a to both sides.
4b=-3ax+4x+15a-2
The equation is in standard form.
\frac{4b}{4}=\frac{-3ax+4x+15a-2}{4}
Divide both sides by 4.
b=\frac{-3ax+4x+15a-2}{4}
Dividing by 4 undoes the multiplication by 4.
b=-\frac{3ax}{4}+\frac{15a}{4}+x-\frac{1}{2}
Divide 4x-2-3ax+15a by 4.
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