Solve ax+b/3=cx+d/2

$$\frac { a x + b } { 3 } = \frac { c x + d } { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{-3cx+2b-3d}{2x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=\frac{3d}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(ax+b\right)=3\left(cx+d\right)$$

Use the distributive property to multiply 2 by ax+b.

$$2ax+2b=3\left(cx+d\right)$$

Use the distributive property to multiply 3 by cx+d.

$$2ax+2b=3cx+3d$$

Subtract 2b from both sides.

$$2ax=3cx+3d-2b$$

The equation is in standard form.

$$2xa=3cx+3d-2b$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{3cx+3d-2b}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{3cx+3d-2b}{2x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{-3cx+2b-3d}{2x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=\frac{3d}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(ax+b\right)=3\left(cx+d\right)$$

Use the distributive property to multiply 2 by ax+b.

$$2ax+2b=3\left(cx+d\right)$$

Use the distributive property to multiply 3 by cx+d.

$$2ax+2b=3cx+3d$$

Subtract 2b from both sides.

$$2ax=3cx+3d-2b$$

The equation is in standard form.

$$2xa=3cx+3d-2b$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{3cx+3d-2b}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{3cx+3d-2b}{2x}$$

Solve for b

$$b=-ax+\frac{3cx}{2}+\frac{3d}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(ax+b\right)=3\left(cx+d\right)$$

Use the distributive property to multiply 2 by ax+b.

$$2ax+2b=3\left(cx+d\right)$$

Use the distributive property to multiply 3 by cx+d.

$$2ax+2b=3cx+3d$$

Subtract 2ax from both sides.

$$2b=3cx+3d-2ax$$

The equation is in standard form.

$$2b=3cx-2ax+3d$$

Divide both sides by 2.

$$\frac{2b}{2}=\frac{3cx-2ax+3d}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$b=\frac{3cx-2ax+3d}{2}$$

Divide 3cx+3d-2ax by 2.

$$b=-ax+\frac{3cx}{2}+\frac{3d}{2}$$