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

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{3 x}{5} - \frac{x - 3}{2}) \cdot 3$ .

To write $\frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

To write $- \frac{x - 3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $2$ .

$(\frac{3 x \cdot 2}{10} - \frac{x - 3}{2} \cdot \frac{5}{5}) \cdot 3 = \frac{x + 2}{3} \cdot 3$

Multiply $\frac{x - 3}{2}$ by $\frac{5}{5}$ .

$(\frac{3 x \cdot 2}{10} - \frac{(x - 3) \cdot 5}{2 \cdot 5}) \cdot 3 = \frac{x + 2}{3} \cdot 3$

Multiply $2$ by $5$ .

$(\frac{3 x \cdot 2}{10} - \frac{(x - 3) \cdot 5}{10}) \cdot 3 = \frac{x + 2}{3} \cdot 3$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - (x - 3) \cdot 5}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 x - (x - 3) \cdot 5}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Apply the distributive property.

$\frac{6 x + (- x - - 3) \cdot 5}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Multiply $- 1$ by $- 3$ .

$\frac{6 x + (- x + 3) \cdot 5}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Apply the distributive property.

$\frac{6 x - x \cdot 5 + 3 \cdot 5}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Multiply $5$ by $- 1$ .

$\frac{6 x - 5 x + 3 \cdot 5}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Multiply $3$ by $5$ .

$\frac{6 x - 5 x + 15}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Subtract $5 x$ from $6 x$ .

$\frac{x + 15}{10} \cdot 3 = \frac{x + 2}{3} \cdot 3$

Combine fractions.

Combine $\frac{x + 15}{10}$ and $3$ .

$\frac{(x + 15) \cdot 3}{10} = \frac{x + 2}{3} \cdot 3$

Move $3$ to the left of $x + 15$ .

$\frac{3 (x + 15)}{10} = \frac{x + 2}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x + 15)}{10} = \frac{x + 2}{3} \cdot 3$

Rewrite the expression.

$\frac{3 (x + 15)}{10} = x + 2$

Step 3

Solve for $x$ .

Multiply both sides by $10$ .

$\frac{3 (x + 15)}{10} \cdot 10 = (x + 2) \cdot 10$

Simplify.

Simplify the left side.

Simplify $\frac{3 (x + 15)}{10} \cdot 10$ .

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{3 (x + 15)}{10} \cdot 10 = (x + 2) \cdot 10$

Rewrite the expression.

$3 (x + 15) = (x + 2) \cdot 10$

Apply the distributive property.

$3 x + 3 \cdot 15 = (x + 2) \cdot 10$

Multiply $3$ by $15$ .

$3 x + 45 = (x + 2) \cdot 10$

Simplify the right side.

Simplify $(x + 2) \cdot 10$ .

Apply the distributive property.

$3 x + 45 = x \cdot 10 + 2 \cdot 10$

Simplify the expression.

Move $10$ to the left of $x$ .

$3 x + 45 = 10 \cdot x + 2 \cdot 10$

Multiply $2$ by $10$ .

$3 x + 45 = 10 x + 20$

Solve for $x$ .

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

Subtract $10 x$ from both sides of the equation.

$3 x + 45 - 10 x = 20$

Subtract $10 x$ from $3 x$ .

$- 7 x + 45 = 20$

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

Subtract $45$ from both sides of the equation.

$- 7 x = 20 - 45$

Subtract $45$ from $20$ .

$- 7 x = - 25$

Divide each term in $- 7 x = - 25$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 25$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 25}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 25}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 25}{- 7}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{25}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{7}$

Decimal Form:

$x = 3.\overline{571428}$

Mixed Number Form:

$x = 3 \frac{4}{7}$

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

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