Solve for x x/3+(5x)/6=1

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

Step 1

Simplify $\frac{x}{3} + \frac{5 x}{6}$ .

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

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

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $2$ to the left of $x$ .

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

Add $2 x$ and $5 x$ .

$\frac{7 x}{6} = 1$

Step 2

Multiply both sides of the equation by $\frac{6}{7}$ .

$\frac{6}{7} \cdot \frac{7 x}{6} = \frac{6}{7} \cdot 1$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{7} \cdot \frac{7 x}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{7} \cdot \frac{7 x}{6} = \frac{6}{7} \cdot 1$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot 1$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{6}{7} \cdot 1$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot 1$

Rewrite the expression.

$x = \frac{6}{7} \cdot 1$

Simplify the right side.

Multiply $\frac{6}{7}$ by $1$ .

$x = \frac{6}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{7}$

Decimal Form:

$x = 0.\overline{857142}$