Solve for x (x+10)/2=7(x-1)

$\frac{x + 10}{2} = 7 (x - 1)$

Multiply both sides by $2$ .

$\frac{x + 10}{2} \cdot 2 = 7 (x - 1) \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x + 10}{2} \cdot 2 = 7 (x - 1) \cdot 2$

Rewrite the expression.

$x + 10 = 7 (x - 1) \cdot 2$

Simplify the right side.

Simplify $7 (x - 1) \cdot 2$ .

Apply the distributive property.

$x + 10 = (7 x + 7 \cdot - 1) \cdot 2$

Multiply $7$ by $- 1$ .

$x + 10 = (7 x - 7) \cdot 2$

Apply the distributive property.

$x + 10 = 7 x \cdot 2 - 7 \cdot 2$

Multiply.

Multiply $2$ by $7$ .

$x + 10 = 14 x - 7 \cdot 2$

Multiply $- 7$ by $2$ .

$x + 10 = 14 x - 14$

Solve for $x$ .

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

Subtract $14 x$ from both sides of the equation.

$x + 10 - 14 x = - 14$

Subtract $14 x$ from $x$ .

$- 13 x + 10 = - 14$

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

Subtract $10$ from both sides of the equation.

$- 13 x = - 14 - 10$

Subtract $10$ from $- 14$ .

$- 13 x = - 24$

Divide each term in $- 13 x = - 24$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 24$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 24}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 24}{- 13}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 13}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{24}{13}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{13}$

Decimal Form:

$x = 1.\overline{846153}$

Mixed Number Form:

$x = 1 \frac{11}{13}$

Solve for x (x+10)/2=7(x-1)

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