Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{b-12x}{2-3x}\text{, }&x\neq \frac{2}{3}\\a\in \mathrm{C}\text{, }&b=8\text{ and }x=\frac{2}{3}\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{b-12x}{2-3x}\text{, }&x\neq \frac{2}{3}\\a\in \mathrm{R}\text{, }&b=8\text{ and }x=\frac{2}{3}\end{matrix}\right.
Solve for b
b=3ax+12x-2a
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b-12x=3ax-2a
Use the distributive property to multiply a by 3x-2.
3ax-2a=b-12x
Swap sides so that all variable terms are on the left hand side.
\left(3x-2\right)a=b-12x
Combine all terms containing a.
\frac{\left(3x-2\right)a}{3x-2}=\frac{b-12x}{3x-2}
Divide both sides by 3x-2.
a=\frac{b-12x}{3x-2}
Dividing by 3x-2 undoes the multiplication by 3x-2.
b-12x=3ax-2a
Use the distributive property to multiply a by 3x-2.
3ax-2a=b-12x
Swap sides so that all variable terms are on the left hand side.
\left(3x-2\right)a=b-12x
Combine all terms containing a.
\frac{\left(3x-2\right)a}{3x-2}=\frac{b-12x}{3x-2}
Divide both sides by 3x-2.
a=\frac{b-12x}{3x-2}
Dividing by 3x-2 undoes the multiplication by 3x-2.
b-12x=3ax-2a
Use the distributive property to multiply a by 3x-2.
b=3ax-2a+12x
Add 12x to both sides.
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Limits
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