Solve for x 2x-1/3=-x/4+6

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

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

Add $\frac{x}{4}$ to both sides of the equation.

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

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Combine $2 x$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $2 x \cdot 4 + x$ .

Factor $x$ out of $2 x \cdot 4$ .

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

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

$\frac{x (2 \cdot 4) + x^{1}}{4} - \frac{1}{3} = 6$

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

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

Factor $x$ out of $x (2 \cdot 4) + x \cdot 1$ .

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

Multiply $2$ by $4$ .

$\frac{x (8 + 1)}{4} - \frac{1}{3} = 6$

Add $8$ and $1$ .

$\frac{x \cdot 9}{4} - \frac{1}{3} = 6$

Move $9$ to the left of $x$ .

$\frac{9 x}{4} - \frac{1}{3} = 6$

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

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

$\frac{9 x}{4} = 6 + \frac{1}{3}$

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9 x}{4} = 6 \cdot \frac{3}{3} + \frac{1}{3}$

Combine $6$ and $\frac{3}{3}$ .

$\frac{9 x}{4} = \frac{6 \cdot 3}{3} + \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{9 x}{4} = \frac{6 \cdot 3 + 1}{3}$

Simplify the numerator.

Multiply $6$ by $3$ .

$\frac{9 x}{4} = \frac{18 + 1}{3}$

Add $18$ and $1$ .

$\frac{9 x}{4} = \frac{19}{3}$

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} \cdot \frac{9 x}{4} = \frac{4}{9} \cdot \frac{19}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{9} \cdot \frac{9 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 x}{4} = \frac{4}{9} \cdot \frac{19}{3}$

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{4}{9} \cdot \frac{19}{3}$

Cancel the common factor of $9$ .

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{4}{9} \cdot \frac{19}{3}$

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{4}{9} \cdot \frac{19}{3}$

Rewrite the expression.

$x = \frac{4}{9} \cdot \frac{19}{3}$

Simplify the right side.

Multiply $\frac{4}{9} \cdot \frac{19}{3}$ .

Multiply $\frac{4}{9}$ by $\frac{19}{3}$ .

$x = \frac{4 \cdot 19}{9 \cdot 3}$

Multiply $4$ by $19$ .

$x = \frac{76}{9 \cdot 3}$

Multiply $9$ by $3$ .

$x = \frac{76}{27}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{76}{27}$

Decimal Form:

$x = 2.\overline{814}$

Mixed Number Form:

$x = 2 \frac{22}{27}$

Solve for x 2x-1/3=-x/4+6

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