Solve the Rational Equation for x x/5=15+x/3

$\frac{x}{5} = 15 + \frac{x}{3}$

Multiply both sides by $5$ .

$\frac{x}{5} \cdot 5 = (15 + \frac{x}{3}) \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{x}{5} \cdot 5 = (15 + \frac{x}{3}) \cdot 5$

Rewrite the expression.

$x = (15 + \frac{x}{3}) \cdot 5$

Simplify the right side.

Simplify $(15 + \frac{x}{3}) \cdot 5$ .

Simplify terms.

Apply the distributive property.

$x = 15 \cdot 5 + \frac{x}{3} \cdot 5$

Multiply $15$ by $5$ .

$x = 75 + \frac{x}{3} \cdot 5$

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

$x = 75 + \frac{x \cdot 5}{3}$

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

$x = 75 + \frac{5 x}{3}$

Reorder $75$ and $\frac{5 x}{3}$ .

$x = \frac{5 x}{3} + 75$

Solve for $x$ .

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

Subtract $\frac{5 x}{3}$ from both sides of the equation.

$x - \frac{5 x}{3} = 75$

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

$x \cdot \frac{3}{3} - \frac{5 x}{3} = 75$

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

$\frac{x \cdot 3}{3} - \frac{5 x}{3} = 75$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - 5 x}{3} = 75$

Simplify the numerator.

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

$\frac{3 \cdot x - 5 x}{3} = 75$

Subtract $5 x$ from $3 x$ .

$\frac{- 2 x}{3} = 75$

Move the negative in front of the fraction.

$- \frac{2 x}{3} = 75$

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 x}{3}) = - \frac{3}{2} \cdot 75$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 x}{3}) = - \frac{3}{2} \cdot 75$

Move the leading negative in $- \frac{2 x}{3}$ into the numerator.

$\frac{- 3}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot 75$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot 75$

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot 75$

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{3}{2} \cdot 75$

Cancel the common factor of $2$ .

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

$\frac{- 1}{2} (2 (- x)) = - \frac{3}{2} \cdot 75$

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{3}{2} \cdot 75$

Rewrite the expression.

$- - x = - \frac{3}{2} \cdot 75$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{2} \cdot 75$

Multiply $x$ by $1$ .

$x = - \frac{3}{2} \cdot 75$

Simplify the right side.

Simplify $- \frac{3}{2} \cdot 75$ .

Multiply $- \frac{3}{2} \cdot 75$ .

Multiply $75$ by $- 1$ .

$x = - 75 (\frac{3}{2})$

Combine $- 75$ and $\frac{3}{2}$ .

$x = \frac{- 75 \cdot 3}{2}$

Multiply $- 75$ by $3$ .

$x = \frac{- 225}{2}$

Move the negative in front of the fraction.

$x = - \frac{225}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{225}{2}$

Decimal Form:

$x = - 112.5$

Mixed Number Form:

$x = - 112 \frac{1}{2}$

Solve the Rational Equation for x x/5=15+x/3

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