Solve for x 3/4x-2/3=x+5/6

$\frac{3}{4} x - \frac{2}{3} = x + \frac{5}{6}$

Step 1

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

$\frac{3 x}{4} - \frac{2}{3} = x + \frac{5}{6}$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{3 x}{4} - \frac{2}{3} - x = \frac{5}{6}$

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

$\frac{3 x}{4} - x \cdot \frac{4}{4} - \frac{2}{3} = \frac{5}{6}$

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

$\frac{3 x}{4} + \frac{- x \cdot 4}{4} - \frac{2}{3} = \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 4}{4} - \frac{2}{3} = \frac{5}{6}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x - x \cdot 4$ .

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - x \cdot 4}{4} - \frac{2}{3} = \frac{5}{6}$

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

$\frac{x \cdot 3 + x (- 1 \cdot 4)}{4} - \frac{2}{3} = \frac{5}{6}$

Factor $x$ out of $x \cdot 3 + x (- 1 \cdot 4)$ .

$\frac{x (3 - 1 \cdot 4)}{4} - \frac{2}{3} = \frac{5}{6}$

Multiply $- 1$ by $4$ .

$\frac{x (3 - 4)}{4} - \frac{2}{3} = \frac{5}{6}$

Subtract $4$ from $3$ .

$\frac{x \cdot - 1}{4} - \frac{2}{3} = \frac{5}{6}$

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

$\frac{- 1 \cdot x}{4} - \frac{2}{3} = \frac{5}{6}$

Move the negative in front of the fraction.

$- \frac{x}{4} - \frac{2}{3} = \frac{5}{6}$

Step 3

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

Add $\frac{2}{3}$ to both sides of the equation.

$- \frac{x}{4} = \frac{5}{6} + \frac{2}{3}$

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

$- \frac{x}{4} = \frac{5}{6} + \frac{2}{3} \cdot \frac{2}{2}$

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

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

$- \frac{x}{4} = \frac{5}{6} + \frac{2 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$- \frac{x}{4} = \frac{5}{6} + \frac{2 \cdot 2}{6}$

Combine the numerators over the common denominator.

$- \frac{x}{4} = \frac{5 + 2 \cdot 2}{6}$

Simplify the numerator.

Multiply $2$ by $2$ .

$- \frac{x}{4} = \frac{5 + 4}{6}$

Add $5$ and $4$ .

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

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Multiply both sides of the equation by $- 4$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Simplify $- 4 (\frac{3}{2})$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$x = - 6$

Solve for x 3/4x-2/3=x+5/6

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