Solve 2px+7/7=1/5(5-x)

$$2 p \frac { x + 7 } { 7 } = \frac { 1 } { 5 } ( 5 - x )$$

Solve for p

$$p=-\frac{7\left(x-5\right)}{10\left(x+7\right)}$$

$$x\neq -7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 35, the least common multiple of 7,5.

$$10p\left(x+7\right)=7\left(5-x\right)$$

Use the distributive property to multiply 10p by x+7.

$$10px+70p=7\left(5-x\right)$$

Use the distributive property to multiply 7 by 5-x.

$$10px+70p=35-7x$$

Combine all terms containing p.

$$\left(10x+70\right)p=35-7x$$

Divide both sides by 10x+70.

$$\frac{\left(10x+70\right)p}{10x+70}=\frac{35-7x}{10x+70}$$

Dividing by 10x+70 undoes the multiplication by 10x+70.

$$p=\frac{35-7x}{10x+70}$$

Divide 35-7x by 10x+70.

$$p=\frac{7\left(5-x\right)}{10\left(x+7\right)}$$

Solve for x

$$x=-\frac{35\left(2p-1\right)}{10p+7}$$

$$p\neq -\frac{7}{10}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 35, the least common multiple of 7,5.

$$10p\left(x+7\right)=7\left(5-x\right)$$

Use the distributive property to multiply 10p by x+7.

$$10px+70p=7\left(5-x\right)$$

Use the distributive property to multiply 7 by 5-x.

$$10px+70p=35-7x$$

Add 7x to both sides.

$$10px+70p+7x=35$$

Subtract 70p from both sides.

$$10px+7x=35-70p$$

Combine all terms containing x.

$$\left(10p+7\right)x=35-70p$$

Divide both sides by 10p+7.

$$\frac{\left(10p+7\right)x}{10p+7}=\frac{35-70p}{10p+7}$$

Dividing by 10p+7 undoes the multiplication by 10p+7.

$$x=\frac{35-70p}{10p+7}$$

Divide 35-70p by 10p+7.

$$x=\frac{35\left(1-2p\right)}{10p+7}$$