Solve for x 1/2x-1/3=4-x

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

Step 1

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

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

Step 2

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

Add $x$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

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

Reorder $x$ and $2$ .

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

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

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

Step 3

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

Add $\frac{1}{3}$ to both sides of the equation.

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

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

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

Combine $4$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $3$ .

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

Add $12$ and $1$ .

$\frac{3 x}{2} = \frac{13}{3}$

Step 4

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot \frac{13}{3}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot \frac{13}{3}$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{13}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot \frac{13}{3}$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{13}{3}$

Rewrite the expression.

$x = \frac{2}{3} \cdot \frac{13}{3}$

Simplify the right side.

Multiply $\frac{2}{3} \cdot \frac{13}{3}$ .

Multiply $\frac{2}{3}$ by $\frac{13}{3}$ .

$x = \frac{2 \cdot 13}{3 \cdot 3}$

Multiply $2$ by $13$ .

$x = \frac{26}{3 \cdot 3}$

Multiply $3$ by $3$ .

$x = \frac{26}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{26}{9}$

Decimal Form:

$x = 2.\overline{8}$

Mixed Number Form:

$x = 2 \frac{8}{9}$

Solve for x 1/2x-1/3=4-x

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