Solve operatorname{lon}x-3/5=x+1/3-2

$$\operatorname { lon } \frac { x - 3 } { 5 } = \frac { x + 1 } { 3 } - 2$$

Solve for l (complex solution)

$$\left\{\begin{matrix}l=-\frac{5\left(5-x\right)}{3no\left(x-3\right)}\text{, }&n\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\l\in \mathrm{C}\text{, }&\left(o=0\text{ or }n=0\right)\text{ and }x=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Use the distributive property to multiply 3lon by x-3.

$$3lonx-9lon=5\left(x+1\right)-30$$

Use the distributive property to multiply 5 by x+1.

$$3lonx-9lon=5x+5-30$$

Subtract 30 from 5 to get -25.

$$3lonx-9lon=5x-25$$

Combine all terms containing l.

$$\left(3onx-9on\right)l=5x-25$$

The equation is in standard form.

$$\left(3nox-9no\right)l=5x-25$$

Divide both sides by 3nxo-9on.

$$\frac{\left(3nox-9no\right)l}{3nox-9no}=\frac{5x-25}{3nox-9no}$$

Dividing by 3nxo-9on undoes the multiplication by 3nxo-9on.

$$l=\frac{5x-25}{3nox-9no}$$

Divide -25+5x by 3nxo-9on.

$$l=\frac{5\left(x-5\right)}{3no\left(x-3\right)}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{5\left(5-x\right)}{3lo\left(x-3\right)}\text{, }&l\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\n\in \mathrm{C}\text{, }&\left(o=0\text{ or }l=0\right)\text{ and }x=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Use the distributive property to multiply 3lon by x-3.

$$3lonx-9lno=5\left(x+1\right)-30$$

Use the distributive property to multiply 5 by x+1.

$$3lonx-9lno=5x+5-30$$

Subtract 30 from 5 to get -25.

$$3lonx-9lno=5x-25$$

Combine all terms containing n.

$$\left(3lox-9lo\right)n=5x-25$$

Divide both sides by 3lxo-9ol.

$$\frac{\left(3lox-9lo\right)n}{3lox-9lo}=\frac{5x-25}{3lox-9lo}$$

Dividing by 3lxo-9ol undoes the multiplication by 3lxo-9ol.

$$n=\frac{5x-25}{3lox-9lo}$$

Divide -25+5x by 3lxo-9ol.

$$n=\frac{5\left(x-5\right)}{3lo\left(x-3\right)}$$

Solve for l

$$\left\{\begin{matrix}l=-\frac{5\left(5-x\right)}{3no\left(x-3\right)}\text{, }&n\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\l\in \mathrm{R}\text{, }&\left(o=0\text{ or }n=0\right)\text{ and }x=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Use the distributive property to multiply 3lon by x-3.

$$3lonx-9lon=5\left(x+1\right)-30$$

Use the distributive property to multiply 5 by x+1.

$$3lonx-9lon=5x+5-30$$

Subtract 30 from 5 to get -25.

$$3lonx-9lon=5x-25$$

Combine all terms containing l.

$$\left(3onx-9on\right)l=5x-25$$

The equation is in standard form.

$$\left(3nox-9no\right)l=5x-25$$

Divide both sides by 3nxo-9on.

$$\frac{\left(3nox-9no\right)l}{3nox-9no}=\frac{5x-25}{3nox-9no}$$

Dividing by 3nxo-9on undoes the multiplication by 3nxo-9on.

$$l=\frac{5x-25}{3nox-9no}$$

Divide -25+5x by 3nxo-9on.

$$l=\frac{5\left(x-5\right)}{3no\left(x-3\right)}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{5\left(5-x\right)}{3lo\left(x-3\right)}\text{, }&l\neq 0\text{ and }o\neq 0\text{ and }x\neq 3\\n\in \mathrm{R}\text{, }&\left(o=0\text{ or }l=0\right)\text{ and }x=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3lon\left(x-3\right)=5\left(x+1\right)-30$$

Use the distributive property to multiply 3lon by x-3.

$$3lonx-9lno=5\left(x+1\right)-30$$

Use the distributive property to multiply 5 by x+1.

$$3lonx-9lno=5x+5-30$$

Subtract 30 from 5 to get -25.

$$3lonx-9lno=5x-25$$

Combine all terms containing n.

$$\left(3lox-9lo\right)n=5x-25$$

Divide both sides by 3lxo-9ol.

$$\frac{\left(3lox-9lo\right)n}{3lox-9lo}=\frac{5x-25}{3lox-9lo}$$

Dividing by 3lxo-9ol undoes the multiplication by 3lxo-9ol.

$$n=\frac{5x-25}{3lox-9lo}$$

Divide -25+5x by 3lxo-9ol.

$$n=\frac{5\left(x-5\right)}{3lo\left(x-3\right)}$$