Solve for n 7/x-3/2=(n-mx)/(px)

$\frac{7}{x} - \frac{3}{2} = \frac{n - m x}{p x}$

Step 1

Rewrite the equation as $\frac{n - m x}{p x} = \frac{7}{x} - \frac{3}{2}$ .

$\frac{n - m x}{p x} = \frac{7}{x} - \frac{3}{2}$

Step 2

Multiply both sides by $p x$ .

$\frac{n - m x}{p x} (p x) = (\frac{7}{x} - \frac{3}{2}) (p x)$

Step 3

Simplify.

Simplify the left side.

Simplify $\frac{n - m x}{p x} (p x)$ .

Cancel the common factor of $p x$ .

Cancel the common factor.

$\frac{n - m x}{p x} (p x) = (\frac{7}{x} - \frac{3}{2}) (p x)$

Rewrite the expression.

$n - m x = (\frac{7}{x} - \frac{3}{2}) (p x)$

Reorder $n$ and $- m x$ .

$- m x + n = (\frac{7}{x} - \frac{3}{2}) (p x)$

Simplify the right side.

Simplify $(\frac{7}{x} - \frac{3}{2}) (p x)$ .

Apply the distributive property.

$- m x + n = \frac{7}{x} (p x) - \frac{3}{2} (p x)$

Cancel the common factor of $x$ .

Factor $x$ out of $p x$ .

$- m x + n = \frac{7}{x} (x p) - \frac{3}{2} (p x)$

Cancel the common factor.

$- m x + n = \frac{7}{x} (x p) - \frac{3}{2} (p x)$

Rewrite the expression.

$- m x + n = 7 p - \frac{3}{2} (p x)$

Multiply $- \frac{3}{2} (p x)$ .

Combine $p$ and $\frac{3}{2}$ .

$- m x + n = 7 p - \frac{p \cdot 3}{2} x$

Combine $x$ and $\frac{p \cdot 3}{2}$ .

$- m x + n = 7 p - \frac{x (p \cdot 3)}{2}$

Move $3$ to the left of $x p$ .

$- m x + n = 7 p - \frac{3 x p}{2}$

Simplify the expression.

Move $x$ .

$- m x + n = 7 p - \frac{3 p x}{2}$

Reorder $7 p$ and $- \frac{3 p x}{2}$ .

$- m x + n = - \frac{3 p x}{2} + 7 p$

Step 4

Add $m x$ to both sides of the equation.

$n = - \frac{3 p x}{2} + 7 p + m x$