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

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

Step 1

Simplify $\frac{3 x}{5} - \frac{x}{3}$ .

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

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

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

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

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $3$ .

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

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

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

Multiply $3$ by $5$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

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

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

$\frac{x (3 \cdot 3) + x (- 1 \cdot 5)}{15} = - 3$

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

$\frac{x (3 \cdot 3 - 1 \cdot 5)}{15} = - 3$

Multiply $3$ by $3$ .

$\frac{x (9 - 1 \cdot 5)}{15} = - 3$

Multiply $- 1$ by $5$ .

$\frac{x (9 - 5)}{15} = - 3$

Subtract $5$ from $9$ .

$\frac{x \cdot 4}{15} = - 3$

Move $4$ to the left of $x$ .

$\frac{4 x}{15} = - 3$

Step 2

Multiply both sides of the equation by $\frac{15}{4}$ .

$\frac{15}{4} \cdot \frac{4 x}{15} = \frac{15}{4} \cdot - 3$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{15}{4} \cdot \frac{4 x}{15}$ .

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15}{4} \cdot \frac{4 x}{15} = \frac{15}{4} \cdot - 3$

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{15}{4} \cdot - 3$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{15}{4} \cdot - 3$

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{15}{4} \cdot - 3$

Rewrite the expression.

$x = \frac{15}{4} \cdot - 3$

Simplify the right side.

Simplify $\frac{15}{4} \cdot - 3$ .

Multiply $\frac{15}{4} \cdot - 3$ .

Combine $\frac{15}{4}$ and $- 3$ .

$x = \frac{15 \cdot - 3}{4}$

Multiply $15$ by $- 3$ .

$x = \frac{- 45}{4}$

Move the negative in front of the fraction.

$x = - \frac{45}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{45}{4}$

Decimal Form:

$x = - 11.25$

Mixed Number Form:

$x = - 11 \frac{1}{4}$

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

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