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

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

Step 1

Multiply both sides by $5$ .

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

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $(\frac{2 x}{3} + 1) \cdot 5$ .

Apply the distributive property.

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

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

Combine $\frac{2 x}{3}$ and $5$ .

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

Multiply $5$ by $2$ .

$3 x = \frac{10 x}{3} + 1 \cdot 5$

Multiply $5$ by $1$ .

$3 x = \frac{10 x}{3} + 5$

Step 3

Solve for $x$ .

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

Subtract $\frac{10 x}{3}$ from both sides of the equation.

$3 x - \frac{10 x}{3} = 5$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $3 x \cdot 3 - 10 x$ .

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

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

Factor $x$ out of $- 10 x$ .

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

Factor $x$ out of $x (3 \cdot 3) + x \cdot - 10$ .

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

Multiply $3$ by $3$ .

$\frac{x (9 - 10)}{3} = 5$

Subtract $10$ from $9$ .

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

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

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

Move the negative in front of the fraction.

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

Multiply both sides of the equation by $- 3$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 3 \cdot 5$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot 5$

Multiply $x$ by $1$ .

$x = - 3 \cdot 5$

Simplify the right side.

Multiply $- 3$ by $5$ .

$x = - 15$

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

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