Find All Complex Solutions 1/2(x+12)=4x-1

$\frac{1}{2} (x + 12) = 4 x - 1$

Multiply each term in $\frac{1}{2} (x + 12) = 4 x - 1$ by $2$ to eliminate the fractions.

Multiply each term in $\frac{1}{2} (x + 12) = 4 x - 1$ by $2$ .

$\frac{1}{2} (x + 12) \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Simplify the left side.

Apply the distributive property.

$(\frac{1}{2} x + \frac{1}{2} \cdot 12) \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Combine $\frac{1}{2}$ and $x$ .

$(\frac{x}{2} + \frac{1}{2} \cdot 12) \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$(\frac{x}{2} + \frac{1}{2} \cdot (2 (6))) \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Cancel the common factor.

$(\frac{x}{2} + \frac{1}{2} \cdot (2 \cdot 6)) \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Rewrite the expression.

$(\frac{x}{2} + 6) \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Apply the distributive property.

$\frac{x}{2} \cdot 2 + 6 \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 + 6 \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Rewrite the expression.

$x + 6 \cdot 2 = 4 x \cdot 2 - 1 \cdot 2$

Multiply $6$ by $2$ .

$x + 12 = 4 x \cdot 2 - 1 \cdot 2$

Simplify the right side.

Simplify each term.

Multiply $2$ by $4$ .

$x + 12 = 8 x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$x + 12 = 8 x - 2$

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

Subtract $8 x$ from both sides of the equation.

$x + 12 - 8 x = - 2$

Subtract $8 x$ from $x$ .

$- 7 x + 12 = - 2$

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

Subtract $12$ from both sides of the equation.

$- 7 x = - 2 - 12$

Subtract $12$ from $- 2$ .

$- 7 x = - 14$

Divide each term in $- 7 x = - 14$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 14$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 14}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 14}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 7}$

Simplify the right side.

Divide $- 14$ by $- 7$ .

$x = 2$

Find All Complex Solutions 1/2(x+12)=4x-1

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