Solve for x 5/6x-2/3=1

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

Step 1

Combine $\frac{5}{6}$ and $x$ .

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

Step 2

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

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

$\frac{5 x}{6} = 1 + \frac{2}{3}$

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $3$ and $2$ .

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

Step 3

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

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{5}{3}$

Step 4

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.

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{5}{3}$

Rewrite the expression.

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

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{6}{5} \cdot \frac{5}{3}$

Simplify the right side.

Simplify $\frac{6}{5} \cdot \frac{5}{3}$ .

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$x = \frac{3 (2)}{5} \cdot \frac{5}{3}$

Cancel the common factor.

$x = \frac{3 \cdot 2}{5} \cdot \frac{5}{3}$

Rewrite the expression.

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 2$

Solve for x 5/6x-2/3=1

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