Solve 1/lfloor6+1/L=x/8

$$\frac { 1 } { \lfloor 6 } + \frac { 1 } { L } = \frac { x } { 8 }$$

Solve for L

$$L=-\frac{24}{4-3x}$$

$$x\neq \frac{4}{3}$$

Steps for Solving Linear Equation

Variable L cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8L, the least common multiple of L,8.

$$\frac{4}{3}L+8=Lx$$

Subtract Lx from both sides.

$$\frac{4}{3}L+8-Lx=0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$\frac{4}{3}L-Lx=-8$$

Combine all terms containing L.

$$\left(\frac{4}{3}-x\right)L=-8$$

Divide both sides by \frac{4}{3}-x.

$$\frac{\left(\frac{4}{3}-x\right)L}{\frac{4}{3}-x}=-\frac{8}{\frac{4}{3}-x}$$

Dividing by \frac{4}{3}-x undoes the multiplication by \frac{4}{3}-x.

$$L=-\frac{8}{\frac{4}{3}-x}$$

Divide -8 by \frac{4}{3}-x.

$$L=-\frac{24}{4-3x}$$

Variable L cannot be equal to 0.

$$L=-\frac{24}{4-3x}\text{, }L\neq 0$$

Solve for x

$$x=\frac{4}{3}+\frac{8}{L}$$

$$L\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8L, the least common multiple of L,8.

$$\frac{4}{3}L+8=Lx$$

Swap sides so that all variable terms are on the left hand side.

$$Lx=\frac{4}{3}L+8$$

The equation is in standard form.

$$Lx=\frac{4L}{3}+8$$

Divide both sides by L.

$$\frac{Lx}{L}=\frac{\frac{4L}{3}+8}{L}$$

Dividing by L undoes the multiplication by L.

$$x=\frac{\frac{4L}{3}+8}{L}$$

Divide 8+\frac{4L}{3} by L.

$$x=\frac{4}{3}+\frac{8}{L}$$