Solve for x (x+51)/2=x-71

$\frac{x + 51}{2} = x - 71$

Multiply both sides by $2$ .

$\frac{x + 51}{2} \cdot 2 = (x - 71) \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x + 51}{2} \cdot 2 = (x - 71) \cdot 2$

Rewrite the expression.

$x + 51 = (x - 71) \cdot 2$

Simplify the right side.

Simplify $(x - 71) \cdot 2$ .

Apply the distributive property.

$x + 51 = x \cdot 2 - 71 \cdot 2$

Simplify the expression.

Move $2$ to the left of $x$ .

$x + 51 = 2 \cdot x - 71 \cdot 2$

Multiply $- 71$ by $2$ .

$x + 51 = 2 x - 142$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$x + 51 - 2 x = - 142$

Subtract $2 x$ from $x$ .

$- x + 51 = - 142$

Move all terms not containing $x$ to the right side of the equation.

Subtract $51$ from both sides of the equation.

$- x = - 142 - 51$

Subtract $51$ from $- 142$ .

$- x = - 193$

Divide each term in $- x = - 193$ by $- 1$ and simplify.

Divide each term in $- x = - 193$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 193}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 193}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 193}{- 1}$

Simplify the right side.

Divide $- 193$ by $- 1$ .

$x = 193$