Solve for x (7-7x)/2=3x-8

$\frac{7 - 7 x}{2} = 3 x - 8$

Step 1

Multiply both sides by $2$ .

$\frac{7 - 7 x}{2} \cdot 2 = (3 x - 8) \cdot 2$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{7 - 7 x}{2} \cdot 2$ .

Factor $7$ out of $7 - 7 x$ .

Factor $7$ out of $7$ .

$\frac{7 (1) - 7 x}{2} \cdot 2 = (3 x - 8) \cdot 2$

Factor $7$ out of $- 7 x$ .

$\frac{7 (1) + 7 (- x)}{2} \cdot 2 = (3 x - 8) \cdot 2$

Factor $7$ out of $7 (1) + 7 (- x)$ .

$\frac{7 (1 - x)}{2} \cdot 2 = (3 x - 8) \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 (1 - x)}{2} \cdot 2 = (3 x - 8) \cdot 2$

Rewrite the expression.

$7 (1 - x) = (3 x - 8) \cdot 2$

Apply the distributive property.

$7 \cdot 1 + 7 (- x) = (3 x - 8) \cdot 2$

Simplify the expression.

Multiply $7$ by $1$ .

$7 + 7 (- x) = (3 x - 8) \cdot 2$

Multiply $- 1$ by $7$ .

$7 - 7 x = (3 x - 8) \cdot 2$

Reorder $7$ and $- 7 x$ .

$- 7 x + 7 = (3 x - 8) \cdot 2$

Simplify the right side.

Simplify $(3 x - 8) \cdot 2$ .

Apply the distributive property.

$- 7 x + 7 = 3 x \cdot 2 - 8 \cdot 2$

Multiply.

Multiply $2$ by $3$ .

$- 7 x + 7 = 6 x - 8 \cdot 2$

Multiply $- 8$ by $2$ .

$- 7 x + 7 = 6 x - 16$

Step 3

Solve for $x$ .

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

Subtract $6 x$ from both sides of the equation.

$- 7 x + 7 - 6 x = - 16$

Subtract $6 x$ from $- 7 x$ .

$- 13 x + 7 = - 16$

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

Subtract $7$ from both sides of the equation.

$- 13 x = - 16 - 7$

Subtract $7$ from $- 16$ .

$- 13 x = - 23$

Divide each term in $- 13 x = - 23$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 23$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 23}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 23}{- 13}$

Divide $x$ by $1$ .

$x = \frac{- 23}{- 13}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{23}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{23}{13}$

Decimal Form:

$x = 1.\overline{769230}$

Mixed Number Form:

$x = 1 \frac{10}{13}$

Solve for x (7-7x)/2=3x-8

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