Solve for x -2(x+4)+6=1/2(x-6)+1

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

Step 1

Simplify $- 2 (x + 4) + 6$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 2$ by $4$ .

$- 2 x - 8 + 6 = \frac{1}{2} \cdot (x - 6) + 1$

Add $- 8$ and $6$ .

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

Step 2

Simplify $\frac{1}{2} \cdot (x - 6) + 1$ .

Simplify each term.

Apply the distributive property.

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 2 x - 2 = \frac{x}{2} - 3 + 1$

Add $- 3$ and $1$ .

$- 2 x - 2 = \frac{x}{2} - 2$

Step 3

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

Subtract $\frac{x}{2}$ from both sides of the equation.

$- 2 x - 2 - \frac{x}{2} = - 2$

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 x \cdot \frac{2}{2} - \frac{x}{2} - 2 = - 2$

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

$\frac{- 2 x \cdot 2}{2} - \frac{x}{2} - 2 = - 2$

Combine the numerators over the common denominator.

$\frac{- 2 x \cdot 2 - x}{2} - 2 = - 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 2 x \cdot 2 - x$ .

Factor $x$ out of $- 2 x \cdot 2$ .

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

Factor $x$ out of $- x$ .

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

Factor $x$ out of $x (- 2 \cdot 2) + x \cdot - 1$ .

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

Multiply $- 2$ by $2$ .

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

Subtract $1$ from $- 4$ .

$\frac{x \cdot - 5}{2} - 2 = - 2$

Move $- 5$ to the left of $x$ .

$\frac{- 5 \cdot x}{2} - 2 = - 2$

Move the negative in front of the fraction.

$- \frac{5 x}{2} - 2 = - 2$

Step 4

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

Add $2$ to both sides of the equation.

$- \frac{5 x}{2} = - 2 + 2$

Add $- 2$ and $2$ .

$- \frac{5 x}{2} = 0$

Step 5

Set the numerator equal to zero.

$5 x = 0$

Step 6

Divide each term in $5 x = 0$ by $5$ and simplify.

Divide each term in $5 x = 0$ by $5$ .

$\frac{5 x}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

Divide $x$ by $1$ .

$x = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x = 0$

Solve for x -2(x+4)+6=1/2(x-6)+1

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