Solve for x 1/3(x-9)-x=11-5/3x

$\frac{1}{3} (x - 9) - x = 11 - \frac{5}{3} x$

Step 1

Simplify $\frac{1}{3} \cdot (x - 9) - x$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot - 9 - x = 11 - \frac{5}{3} x$

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

$\frac{x}{3} + \frac{1}{3} \cdot - 9 - x = 11 - \frac{5}{3} x$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

$\frac{x}{3} + \frac{1}{3} \cdot (3 (- 3)) - x = 11 - \frac{5}{3} x$

Cancel the common factor.

$\frac{x}{3} + \frac{1}{3} \cdot (3 \cdot - 3) - x = 11 - \frac{5}{3} x$

Rewrite the expression.

$\frac{x}{3} - 3 - x = 11 - \frac{5}{3} x$

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

$\frac{x}{3} - x \cdot \frac{3}{3} - 3 = 11 - \frac{5}{3} x$

Simplify terms.

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

$\frac{x}{3} + \frac{- x \cdot 3}{3} - 3 = 11 - \frac{5}{3} x$

Combine the numerators over the common denominator.

$\frac{x - x \cdot 3}{3} - 3 = 11 - \frac{5}{3} x$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x^{1} - x \cdot 3}{3} - 3 = 11 - \frac{5}{3} x$

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

$\frac{x \cdot 1 - x \cdot 3}{3} - 3 = 11 - \frac{5}{3} x$

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

$\frac{x \cdot 1 + x (- 1 \cdot 3)}{3} - 3 = 11 - \frac{5}{3} x$

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

$\frac{x (1 - 1 \cdot 3)}{3} - 3 = 11 - \frac{5}{3} x$

Multiply $- 1$ by $3$ .

$\frac{x (1 - 3)}{3} - 3 = 11 - \frac{5}{3} x$

Subtract $3$ from $1$ .

$\frac{x \cdot - 2}{3} - 3 = 11 - \frac{5}{3} x$

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

$\frac{- 2 \cdot x}{3} - 3 = 11 - \frac{5}{3} x$

Move the negative in front of the fraction.

$- \frac{2 x}{3} - 3 = 11 - \frac{5}{3} x$

Step 2

Simplify each term.

Combine $x$ and $\frac{5}{3}$ .

$- \frac{2 x}{3} - 3 = 11 - \frac{x \cdot 5}{3}$

Move $5$ to the left of $x$ .

$- \frac{2 x}{3} - 3 = 11 - \frac{5 x}{3}$

Step 3

Move all terms containing $x$ to the left side of the equation.

Add $\frac{5 x}{3}$ to both sides of the equation.

$- \frac{2 x}{3} - 3 + \frac{5 x}{3} = 11$

Combine the numerators over the common denominator.

$- 3 + \frac{- 2 x + 5 x}{3} = 11$

Add $- 2 x$ and $5 x$ .

$- 3 + \frac{3 x}{3} = 11$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 3 + \frac{3 x}{3} = 11$

Divide $x$ by $1$ .

$- 3 + x = 11$

Step 4

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

Add $3$ to both sides of the equation.

$x = 11 + 3$

Add $11$ and $3$ .

$x = 14$

Solve for x 1/3(x-9)-x=11-5/3x

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