Solve for x (2x)/3+x/2=1/6

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

Step 1

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

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

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

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

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $2 x \cdot 2 + x \cdot 3$ .

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

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

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

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

Factor $x$ out of $x (2 \cdot 2) + x (3)$ .

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

Multiply $2$ by $2$ .

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

Add $4$ and $3$ .

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

Move $7$ to the left of $x$ .

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

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 x = 1$

Step 3

Divide each term in $7 x = 1$ by $7$ and simplify.

Divide each term in $7 x = 1$ by $7$ .

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{142857}$

Solve for x (2x)/3+x/2=1/6

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