Solve for x 5/3x-3=1/3+2x

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

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

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

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

Subtract $2 x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - 2 x \cdot 3$ .

Factor $x$ out of $5 x$ .

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

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

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

Factor $x$ out of $x \cdot 5 + x (- 2 \cdot 3)$ .

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

Multiply $- 2$ by $3$ .

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

Subtract $6$ from $5$ .

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

Move $- 1$ to the left of $x$ .

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

Move the negative in front of the fraction.

$- \frac{x}{3} - 3 = \frac{1}{3}$

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

Add $3$ to both sides of the equation.

$- \frac{x}{3} = \frac{1}{3} + 3$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $3$ .

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

Add $1$ and $9$ .

$- \frac{x}{3} = \frac{10}{3}$

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

$- x = 10$

Divide each term in $- x = 10$ by $- 1$ and simplify.

Divide each term in $- x = 10$ by $- 1$ .

$\frac{- x}{- 1} = \frac{10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{10}{- 1}$

Divide $x$ by $1$ .

$x = \frac{10}{- 1}$

Simplify the right side.

Divide $10$ by $- 1$ .

$x = - 10$

Solve for x 5/3x-3=1/3+2x

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