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

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

Step 1

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

Subtract $x$ from both sides of the equation.

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

To write $- x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $3 x$ .

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

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

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

Factor $x$ out of $x \cdot 3 + x (- 1 \cdot 5)$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $3$ .

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

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

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

Move the negative in front of the fraction.

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

Step 2

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

Add $2$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$- \frac{2 x}{5} = \frac{1 + 6}{3}$

Add $1$ and $6$ .

$- \frac{2 x}{5} = \frac{7}{3}$

Step 3

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} \cdot \frac{7}{3}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{2} (- \frac{2 x}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} \cdot \frac{7}{3}$

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot \frac{7}{3}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot \frac{7}{3}$

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot \frac{7}{3}$

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{5}{2} \cdot \frac{7}{3}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} \cdot \frac{7}{3}$

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} \cdot \frac{7}{3}$

Rewrite the expression.

$- - x = - \frac{5}{2} \cdot \frac{7}{3}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{2} \cdot \frac{7}{3}$

Multiply $x$ by $1$ .

$x = - \frac{5}{2} \cdot \frac{7}{3}$

Simplify the right side.

Multiply $- \frac{5}{2} \cdot \frac{7}{3}$ .

Multiply $\frac{7}{3}$ by $\frac{5}{2}$ .

$x = - \frac{7 \cdot 5}{3 \cdot 2}$

Multiply $7$ by $5$ .

$x = - \frac{35}{3 \cdot 2}$

Multiply $3$ by $2$ .

$x = - \frac{35}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{35}{6}$

Decimal Form:

$x = - 5.8\overline{3}$

Mixed Number Form:

$x = - 5 \frac{5}{6}$

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

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