Solve for x 2x+x/3=7/3

$2 x + \frac{x}{3} = \frac{7}{3}$

Step 1

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

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

$2 x \cdot \frac{3}{3} + \frac{x}{3} = \frac{7}{3}$

Simplify terms.

Combine $2 x$ and $\frac{3}{3}$ .

$\frac{2 x \cdot 3}{3} + \frac{x}{3} = \frac{7}{3}$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 + x}{3} = \frac{7}{3}$

Simplify the numerator.

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

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

$\frac{x (2 \cdot 3) + x}{3} = \frac{7}{3}$

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

$\frac{x (2 \cdot 3) + x^{1}}{3} = \frac{7}{3}$

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

$\frac{x (2 \cdot 3) + x \cdot 1}{3} = \frac{7}{3}$

Factor $x$ out of $x (2 \cdot 3) + x \cdot 1$ .

$\frac{x (2 \cdot 3 + 1)}{3} = \frac{7}{3}$

Multiply $2$ by $3$ .

$\frac{x (6 + 1)}{3} = \frac{7}{3}$

Add $6$ and $1$ .

$\frac{x \cdot 7}{3} = \frac{7}{3}$

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

$\frac{7 x}{3} = \frac{7}{3}$

Step 2

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

$7 x = 7$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $7$ by $7$ .

$x = 1$