Solve for x ax+b=3(x-a)

$a x + b = 3 (x - a)$

Step 1

Simplify $3 (x - a)$ .

Rewrite.

$a x + b = 0 + 0 + 3 (x - a)$

Simplify by adding zeros.

$a x + b = 3 (x - a)$

Apply the distributive property.

$a x + b = 3 x + 3 (- a)$

Multiply $- 1$ by $3$ .

$a x + b = 3 x - 3 a$

Step 2

Subtract $3 x$ from both sides of the equation.

$a x + b - 3 x = - 3 a$

Step 3

Subtract $b$ from both sides of the equation.

$a x - 3 x = - 3 a - b$

Step 4

Factor $x$ out of $a x - 3 x$ .

Factor $x$ out of $a x$ .

$x a - 3 x = - 3 a - b$

Factor $x$ out of $- 3 x$ .

$x a + x \cdot - 3 = - 3 a - b$

Factor $x$ out of $x a + x \cdot - 3$ .

$x (a - 3) = - 3 a - b$

Step 5

Divide each term in $x (a - 3) = - 3 a - b$ by $a - 3$ and simplify.

Divide each term in $x (a - 3) = - 3 a - b$ by $a - 3$ .

$\frac{x (a - 3)}{a - 3} = \frac{- 3 a}{a - 3} + \frac{- b}{a - 3}$

Simplify the left side.

Cancel the common factor of $a - 3$ .

Cancel the common factor.

$\frac{x (a - 3)}{a - 3} = \frac{- 3 a}{a - 3} + \frac{- b}{a - 3}$

Divide $x$ by $1$ .

$x = \frac{- 3 a}{a - 3} + \frac{- b}{a - 3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{(3) a}{a - 3} + \frac{- b}{a - 3}$

Move the negative in front of the fraction.

$x = - \frac{3 a}{a - 3} - \frac{b}{a - 3}$

Simplify terms.

Combine the numerators over the common denominator.

$x = \frac{- 3 a - b}{a - 3}$

Factor $- 1$ out of $- 3 a$ .

$x = \frac{- (3 a) - b}{a - 3}$

Factor $- 1$ out of $- b$ .

$x = \frac{- (3 a) - (b)}{a - 3}$

Factor $- 1$ out of $- (3 a) - (b)$ .

$x = \frac{- (3 a + b)}{a - 3}$

Simplify the expression.

Rewrite $- (3 a + b)$ as $- 1 (3 a + b)$ .

$x = \frac{- 1 (3 a + b)}{a - 3}$

Move the negative in front of the fraction.

$x = - \frac{3 a + b}{a - 3}$

Solve for x ax+b=3(x-a)

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