Solve for x (1-x)/3=a

$\frac{1 - x}{3} = a$

Step 1

Multiply both sides by $3$ .

$\frac{1 - x}{3} \cdot 3 = a \cdot 3$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{1 - x}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1 - x}{3} \cdot 3 = a \cdot 3$

Rewrite the expression.

$1 - x = a \cdot 3$

Reorder $1$ and $- x$ .

$- x + 1 = a \cdot 3$

Simplify the right side.

Move $3$ to the left of $a$ .

$- x + 1 = 3 a$

Step 3

Solve for $x$ .

Subtract $1$ from both sides of the equation.

$- x = 3 a - 1$

Divide each term in $- x = 3 a - 1$ by $- 1$ and simplify.

Divide each term in $- x = 3 a - 1$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{3 a}{- 1}$ .

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

Rewrite $- 1 \cdot (3 a)$ as $- (3 a)$ .

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

Multiply $3$ by $- 1$ .

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

Divide $- 1$ by $- 1$ .

$x = - 3 a + 1$