Solve for x x/4+3=1/2(1-x/3)

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

Simplify $\frac{1}{2} \cdot (1 - \frac{x}{3})$ .

Rewrite.

$\frac{x}{4} + 3 = 0 + 0 + \frac{1}{2} \cdot (1 - \frac{x}{3})$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $\frac{1}{2}$ by $1$ .

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

Multiply $\frac{1}{2} (- \frac{x}{3})$ .

Multiply $\frac{1}{2}$ by $\frac{x}{3}$ .

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

Multiply $2$ by $3$ .

$\frac{x}{4} + 3 = \frac{1}{2} - \frac{x}{6}$

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

Add $\frac{x}{6}$ to both sides of the equation.

$\frac{x}{4} + 3 + \frac{x}{6} = \frac{1}{2}$

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{4} \cdot \frac{3}{3} + \frac{x}{6} + 3 = \frac{1}{2}$

To write $\frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} \cdot \frac{3}{3} + \frac{x}{6} \cdot \frac{2}{2} + 3 = \frac{1}{2}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{4}$ by $\frac{3}{3}$ .

$\frac{x \cdot 3}{4 \cdot 3} + \frac{x}{6} \cdot \frac{2}{2} + 3 = \frac{1}{2}$

Multiply $4$ by $3$ .

$\frac{x \cdot 3}{12} + \frac{x}{6} \cdot \frac{2}{2} + 3 = \frac{1}{2}$

Multiply $\frac{x}{6}$ by $\frac{2}{2}$ .

$\frac{x \cdot 3}{12} + \frac{x \cdot 2}{6 \cdot 2} + 3 = \frac{1}{2}$

Multiply $6$ by $2$ .

$\frac{x \cdot 3}{12} + \frac{x \cdot 2}{12} + 3 = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + x \cdot 2}{12} + 3 = \frac{1}{2}$

Reorder $x$ and $2$ .

$\frac{3 \cdot x + 2 \cdot x}{12} + 3 = \frac{1}{2}$

Add $3 \cdot x$ and $2 \cdot x$ .

$\frac{5 x}{12} + 3 = \frac{1}{2}$

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

Subtract $3$ from both sides of the equation.

$\frac{5 x}{12} = \frac{1}{2} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{12} = \frac{1}{2} - 3 \cdot \frac{2}{2}$

Combine $- 3$ and $\frac{2}{2}$ .

$\frac{5 x}{12} = \frac{1}{2} + \frac{- 3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{5 x}{12} = \frac{1 - 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$\frac{5 x}{12} = \frac{1 - 6}{2}$

Subtract $6$ from $1$ .

$\frac{5 x}{12} = \frac{- 5}{2}$

Move the negative in front of the fraction.

$\frac{5 x}{12} = - \frac{5}{2}$

Multiply both sides of the equation by $\frac{12}{5}$ .

$\frac{12}{5} \cdot \frac{5 x}{12} = \frac{12}{5} (- \frac{5}{2})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{5} \cdot \frac{5 x}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{5} \cdot \frac{5 x}{12} = \frac{12}{5} (- \frac{5}{2})$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{12}{5} (- \frac{5}{2})$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{12}{5} (- \frac{5}{2})$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{12}{5} (- \frac{5}{2})$

Rewrite the expression.

$x = \frac{12}{5} (- \frac{5}{2})$

Simplify the right side.

Simplify $\frac{12}{5} (- \frac{5}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x = \frac{12}{5} \cdot \frac{- 5}{2}$

Factor $2$ out of $12$ .

$x = \frac{2 (6)}{5} \cdot \frac{- 5}{2}$

Cancel the common factor.

$x = \frac{2 \cdot 6}{5} \cdot \frac{- 5}{2}$

Rewrite the expression.

$x = \frac{6}{5} \cdot - 5$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$x = \frac{6}{5} \cdot (5 (- 1))$

Cancel the common factor.

$x = \frac{6}{5} \cdot (5 \cdot - 1)$

Rewrite the expression.

$x = 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$x = - 6$

Solve for x x/4+3=1/2(1-x/3)

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