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

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

Step 1

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

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

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

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

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Move $2$ to the left of $x$ .

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

Multiply $- 3$ by $2$ .

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

Apply the distributive property.

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

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

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

Multiply $- 2$ by $3$ .

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

Add $2 x$ and $3 x$ .

$\frac{5 x - 6 - 6}{6} = - 2$

Subtract $6$ from $- 6$ .

$\frac{5 x - 12}{6} = - 2$

Step 2

Multiply both sides by $6$ .

$\frac{5 x - 12}{6} \cdot 6 = - 2 \cdot 6$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{5 x - 12}{6} \cdot 6 = - 2 \cdot 6$

Rewrite the expression.

$5 x - 12 = - 2 \cdot 6$

Simplify the right side.

Multiply $- 2$ by $6$ .

$5 x - 12 = - 12$

Step 4

Solve for $x$ .

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

Add $12$ to both sides of the equation.

$5 x = - 12 + 12$

Add $- 12$ and $12$ .

$5 x = 0$

Divide each term in $5 x = 0$ by $5$ and simplify.

Divide each term in $5 x = 0$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $0$ by $5$ .

$x = 0$

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

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