Solve for x 1/2x+8=3-1/3x

$\frac{1}{2} x + 8 = 3 - \frac{1}{3} x$

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

$\frac{x}{2} + 8 = 3 - \frac{1}{3} x$

Combine $x$ and $\frac{1}{3}$ .

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

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

Add $\frac{x}{3}$ to both sides of the equation.

$\frac{x}{2} + 8 + \frac{x}{3} = 3$

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

$\frac{x}{2} \cdot \frac{3}{3} + \frac{x}{3} + 8 = 3$

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

$\frac{x}{2} \cdot \frac{3}{3} + \frac{x}{3} \cdot \frac{2}{2} + 8 = 3$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{x \cdot 3}{2 \cdot 3} + \frac{x}{3} \cdot \frac{2}{2} + 8 = 3$

Multiply $2$ by $3$ .

$\frac{x \cdot 3}{6} + \frac{x}{3} \cdot \frac{2}{2} + 8 = 3$

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

$\frac{x \cdot 3}{6} + \frac{x \cdot 2}{3 \cdot 2} + 8 = 3$

Multiply $3$ by $2$ .

$\frac{x \cdot 3}{6} + \frac{x \cdot 2}{6} + 8 = 3$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + x \cdot 2}{6} + 8 = 3$

Reorder $x$ and $2$ .

$\frac{3 \cdot x + 2 \cdot x}{6} + 8 = 3$

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

$\frac{5 x}{6} + 8 = 3$

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

Subtract $8$ from both sides of the equation.

$\frac{5 x}{6} = 3 - 8$

Subtract $8$ from $3$ .

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

Multiply both sides of the equation by $\frac{6}{5}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} \cdot \frac{5 x}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{6}{5} \cdot - 5$ .

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 1/2x+8=3-1/3x

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