Solve for x 1/3(x-15)+2x=16

$\frac{1}{3} (x - 15) + 2 x = 16$

Step 1

Simplify $\frac{1}{3} \cdot (x - 15) + 2 x$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot - 15 + 2 x = 16$

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

$\frac{x}{3} + \frac{1}{3} \cdot - 15 + 2 x = 16$

Cancel the common factor of $3$ .

Factor $3$ out of $- 15$ .

$\frac{x}{3} + \frac{1}{3} \cdot (3 (- 5)) + 2 x = 16$

Cancel the common factor.

$\frac{x}{3} + \frac{1}{3} \cdot (3 \cdot - 5) + 2 x = 16$

Rewrite the expression.

$\frac{x}{3} - 5 + 2 x = 16$

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

$\frac{x}{3} + 2 x \cdot \frac{3}{3} - 5 = 16$

Simplify terms.

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

$\frac{x}{3} + \frac{2 x \cdot 3}{3} - 5 = 16$

Combine the numerators over the common denominator.

$\frac{x + 2 x \cdot 3}{3} - 5 = 16$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x^{1} + 2 x \cdot 3}{3} - 5 = 16$

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

$\frac{x \cdot 1 + 2 x \cdot 3}{3} - 5 = 16$

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

$\frac{x \cdot 1 + x (2 \cdot 3)}{3} - 5 = 16$

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

$\frac{x (1 + 2 \cdot 3)}{3} - 5 = 16$

Multiply $2$ by $3$ .

$\frac{x (1 + 6)}{3} - 5 = 16$

Add $1$ and $6$ .

$\frac{x \cdot 7}{3} - 5 = 16$

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

$\frac{7 x}{3} - 5 = 16$

Step 2

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

Add $5$ to both sides of the equation.

$\frac{7 x}{3} = 16 + 5$

Add $16$ and $5$ .

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

Step 3

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

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

Step 4

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 1/3(x-15)+2x=16

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