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

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

Step 1

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

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (6 + x) = x + 4$

Simplify by adding zeros.

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{1}{2} \cdot (2 (3)) + \frac{1}{2} x = x + 4$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 3) + \frac{1}{2} x = x + 4$

Rewrite the expression.

$3 + \frac{1}{2} x = x + 4$

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

$3 + \frac{x}{2} = x + 4$

Step 2

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

Subtract $x$ from both sides of the equation.

$3 + \frac{x}{2} - x = 4$

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

$3 + \frac{x}{2} - x \cdot \frac{2}{2} = 4$

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

$3 + \frac{x}{2} + \frac{- x \cdot 2}{2} = 4$

Combine the numerators over the common denominator.

$3 + \frac{x - x \cdot 2}{2} = 4$

Simplify each term.

Simplify the numerator.

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

Raise $x$ to the power of $1$ .

$3 + \frac{x^{1} - x \cdot 2}{2} = 4$

Factor $x$ out of $x^{1}$ .

$3 + \frac{x \cdot 1 - x \cdot 2}{2} = 4$

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

$3 + \frac{x \cdot 1 + x (- 1 \cdot 2)}{2} = 4$

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

$3 + \frac{x (1 - 1 \cdot 2)}{2} = 4$

Multiply $- 1$ by $2$ .

$3 + \frac{x (1 - 2)}{2} = 4$

Subtract $2$ from $1$ .

$3 + \frac{x \cdot - 1}{2} = 4$

Move $- 1$ to the left of $x$ .

$3 + \frac{- 1 \cdot x}{2} = 4$

Move the negative in front of the fraction.

$3 - \frac{x}{2} = 4$

Step 3

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

Subtract $3$ from both sides of the equation.

$- \frac{x}{2} = 4 - 3$

Subtract $3$ from $4$ .

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

Step 4

Multiply both sides of the equation by $- 2$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 2 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot 1$

Multiply $x$ by $1$ .

$x = - 2 \cdot 1$

Simplify the right side.

Multiply $- 2$ by $1$ .

$x = - 2$

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

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