Solve for x x-x/3-x/2-5=0

$x - \frac{x}{3} - \frac{x}{2} - 5 = 0$

Step 1

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

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

$x \cdot \frac{3}{3} - \frac{x}{3} - \frac{x}{2} - 5 = 0$

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

$\frac{x \cdot 3}{3} - \frac{x}{3} - \frac{x}{2} - 5 = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - x}{3} - \frac{x}{2} - 5 = 0$

Subtract $x$ from $x \cdot 3$ .

Reorder $x$ and $3$ .

$\frac{3 \cdot x - x}{3} - \frac{x}{2} - 5 = 0$

Subtract $x$ from $3 \cdot x$ .

$\frac{2 \cdot x}{3} - \frac{x}{2} - 5 = 0$

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

$\frac{2 x}{3} \cdot \frac{2}{2} - \frac{x}{2} - 5 = 0$

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

$\frac{2 x}{3} \cdot \frac{2}{2} - \frac{x}{2} \cdot \frac{3}{3} - 5 = 0$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{2 x \cdot 2}{3 \cdot 2} - \frac{x}{2} \cdot \frac{3}{3} - 5 = 0$

Multiply $3$ by $2$ .

$\frac{2 x \cdot 2}{6} - \frac{x}{2} \cdot \frac{3}{3} - 5 = 0$

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

$\frac{2 x \cdot 2}{6} - \frac{x \cdot 3}{2 \cdot 3} - 5 = 0$

Multiply $2$ by $3$ .

$\frac{2 x \cdot 2}{6} - \frac{x \cdot 3}{6} - 5 = 0$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - x \cdot 3}{6} - 5 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $2 x \cdot 2 - x \cdot 3$ .

Factor $x$ out of $2 x \cdot 2$ .

$\frac{x (2 \cdot 2) - x \cdot 3}{6} - 5 = 0$

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

$\frac{x (2 \cdot 2) + x (- 1 \cdot 3)}{6} - 5 = 0$

Factor $x$ out of $x (2 \cdot 2) + x (- 1 \cdot 3)$ .

$\frac{x (2 \cdot 2 - 1 \cdot 3)}{6} - 5 = 0$

Multiply $2$ by $2$ .

$\frac{x (4 - 1 \cdot 3)}{6} - 5 = 0$

Multiply $- 1$ by $3$ .

$\frac{x (4 - 3)}{6} - 5 = 0$

Subtract $3$ from $4$ .

$\frac{x \cdot 1}{6} - 5 = 0$

Multiply $x$ by $1$ .

$\frac{x}{6} - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

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

Step 3

Multiply both sides of the equation by $6$ .

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 6 \cdot 5$

Simplify the right side.

Multiply $6$ by $5$ .

$x = 30$

Solve for x x-x/3-x/2-5=0

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