Solve for x cx-b=x/a

$c x - b = \frac{x}{a}$

Step 1

Multiply both sides by $a$ .

$(c x - b) a = \frac{x}{a} a$

Step 2

Simplify.

Simplify the left side.

Simplify $(c x - b) a$ .

Apply the distributive property.

$c x a - b a = \frac{x}{a} a$

Simplify the expression.

Move $x$ .

$c a x - b a = \frac{x}{a} a$

Reorder $c$ and $a$ .

$a c x - b a = \frac{x}{a} a$

Move $b$ .

$a c x - 1 a b = \frac{x}{a} a$

Simplify the right side.

Cancel the common factor of $a$ .

Cancel the common factor.

$a c x - 1 a b = \frac{x}{a} a$

Rewrite the expression.

$a c x - 1 a b = x$

Step 3

Solve for $x$ .

Rewrite $- 1 a$ as $- a$ .

$a c x - a b = x$

Subtract $x$ from both sides of the equation.

$a c x - a b - x = 0$

Add $a b$ to both sides of the equation.

$a c x - x = a b$

Factor $x$ out of $a c x - x$ .

Factor $x$ out of $a c x$ .

$x (a c) - x = a b$

Factor $x$ out of $- x$ .

$x (a c) + x \cdot - 1 = a b$

Factor $x$ out of $x (a c) + x \cdot - 1$ .

$x (a c - 1) = a b$

Divide each term in $x (a c - 1) = a b$ by $a c - 1$ and simplify.

Divide each term in $x (a c - 1) = a b$ by $a c - 1$ .

$\frac{x (a c - 1)}{a c - 1} = \frac{a b}{a c - 1}$

Simplify the left side.

Cancel the common factor of $a c - 1$ .

Cancel the common factor.

$\frac{x (a c - 1)}{a c - 1} = \frac{a b}{a c - 1}$

Divide $x$ by $1$ .

$x = \frac{a b}{a c - 1}$

Solve for x cx-b=x/a

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