Solve for x 2x+1/3x=21

$2 x + \frac{1}{3} x = 21$

Step 1

Simplify $2 x + \frac{1}{3} x$ .

Combine $\frac{1}{3}$ and $x$ .

$2 x + \frac{x}{3} = 21$

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

$2 x \cdot \frac{3}{3} + \frac{x}{3} = 21$

Simplify terms.

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

$\frac{2 x \cdot 3}{3} + \frac{x}{3} = 21$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 3 + x}{3} = 21$

Simplify the numerator.

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

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

$\frac{x (2 \cdot 3) + x}{3} = 21$

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

$\frac{x (2 \cdot 3) + x^{1}}{3} = 21$

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

$\frac{x (2 \cdot 3) + x \cdot 1}{3} = 21$

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

$\frac{x (2 \cdot 3 + 1)}{3} = 21$

Multiply $2$ by $3$ .

$\frac{x (6 + 1)}{3} = 21$

Add $6$ and $1$ .

$\frac{x \cdot 7}{3} = 21$

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

$\frac{7 x}{3} = 21$

Step 2

Multiply both sides of the equation by $\frac{3}{7}$ .

$\frac{3}{7} \cdot \frac{7 x}{3} = \frac{3}{7} \cdot 21$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{7} \cdot \frac{7 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{7} \cdot \frac{7 x}{3} = \frac{3}{7} \cdot 21$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{3}{7} \cdot 21$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{3}{7} \cdot 21$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{3}{7} \cdot 21$

Rewrite the expression.

$x = \frac{3}{7} \cdot 21$

Simplify the right side.

Simplify $\frac{3}{7} \cdot 21$ .

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 3 \cdot 3$

Multiply $3$ by $3$ .

$x = 9$

Solve for x 2x+1/3x=21

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