Solve 10Pquad1/4(x+1)=1/5(8-x)

$$10 P \quad \frac { 1 } { 4 } ( x + 1 ) = \frac { 1 } { 5 } ( 8 - x )$$

Solve for P

$$P=-\frac{2\left(x-8\right)}{25\left(x+1\right)}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Multiply 10 and \frac{1}{4} to get \frac{5}{2}.

$$\frac{5}{2}P\left(x+1\right)=\frac{1}{5}\left(8-x\right)$$

Use the distributive property to multiply \frac{5}{2}P by x+1.

$$\frac{5}{2}Px+\frac{5}{2}P=\frac{1}{5}\left(8-x\right)$$

Use the distributive property to multiply \frac{1}{5} by 8-x.

$$\frac{5}{2}Px+\frac{5}{2}P=\frac{8}{5}-\frac{1}{5}x$$

Combine all terms containing P.

$$\left(\frac{5}{2}x+\frac{5}{2}\right)P=\frac{8}{5}-\frac{1}{5}x$$

The equation is in standard form.

$$\frac{5x+5}{2}P=\frac{8-x}{5}$$

Divide both sides by \frac{5}{2}x+\frac{5}{2}.

$$\frac{2\times \frac{5x+5}{2}P}{5x+5}=\frac{8-x}{5\times \frac{5x+5}{2}}$$

Dividing by \frac{5}{2}x+\frac{5}{2} undoes the multiplication by \frac{5}{2}x+\frac{5}{2}.

$$P=\frac{8-x}{5\times \frac{5x+5}{2}}$$

Divide \frac{8-x}{5} by \frac{5}{2}x+\frac{5}{2}.

$$P=\frac{2\left(8-x\right)}{25\left(x+1\right)}$$

Solve for x

$$x=-\frac{25P-16}{25P+2}$$

$$P\neq -\frac{2}{25}$$

Steps for Solving Linear Equation

Multiply 10 and \frac{1}{4} to get \frac{5}{2}.

$$\frac{5}{2}P\left(x+1\right)=\frac{1}{5}\left(8-x\right)$$

Use the distributive property to multiply \frac{5}{2}P by x+1.

$$\frac{5}{2}Px+\frac{5}{2}P=\frac{1}{5}\left(8-x\right)$$

Use the distributive property to multiply \frac{1}{5} by 8-x.

$$\frac{5}{2}Px+\frac{5}{2}P=\frac{8}{5}-\frac{1}{5}x$$

Add \frac{1}{5}x to both sides.

$$\frac{5}{2}Px+\frac{5}{2}P+\frac{1}{5}x=\frac{8}{5}$$

Subtract \frac{5}{2}P from both sides.

$$\frac{5}{2}Px+\frac{1}{5}x=\frac{8}{5}-\frac{5}{2}P$$

Combine all terms containing x.

$$\left(\frac{5}{2}P+\frac{1}{5}\right)x=\frac{8}{5}-\frac{5}{2}P$$

The equation is in standard form.

$$\left(\frac{5P}{2}+\frac{1}{5}\right)x=-\frac{5P}{2}+\frac{8}{5}$$

Divide both sides by \frac{5}{2}P+\frac{1}{5}.

$$\frac{\left(\frac{5P}{2}+\frac{1}{5}\right)x}{\frac{5P}{2}+\frac{1}{5}}=\frac{-\frac{5P}{2}+\frac{8}{5}}{\frac{5P}{2}+\frac{1}{5}}$$

Dividing by \frac{5}{2}P+\frac{1}{5} undoes the multiplication by \frac{5}{2}P+\frac{1}{5}.

$$x=\frac{-\frac{5P}{2}+\frac{8}{5}}{\frac{5P}{2}+\frac{1}{5}}$$

Divide \frac{8}{5}-\frac{5P}{2} by \frac{5}{2}P+\frac{1}{5}.

$$x=\frac{16-25P}{25P+2}$$