Solve for x x/3-(x-1)/2=1

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

Factor the equation.

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

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

To write $- \frac{x - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

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

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

Multiply $3$ by $2$ .

$\frac{x \cdot 2}{6} - \frac{x - 1}{2} \cdot \frac{3}{3} = 1$

Multiply $\frac{x - 1}{2}$ and $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Rewrite $\frac{x \cdot 2 - (x - 1) \cdot 3}{6}$ in a factored form.

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

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

Apply the distributive property.

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

Multiply $- 1$ by $- 1$ .

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

Apply the distributive property.

$\frac{2 x - x \cdot 3 + 1 \cdot 3}{6} = 1$

Multiply $3$ by $- 1$ .

$\frac{2 x - 3 x + 1 \cdot 3}{6} = 1$

Multiply $3$ by $1$ .

$\frac{2 x - 3 x + 3}{6} = 1$

Subtract $3 x$ from $2 x$ .

$\frac{- x + 3}{6} = 1$

Solve the equation.

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Multiply both sides of the equation by $6$ .

$- x + 3 = 1 \cdot (6)$

Remove parentheses.

$- x + 3 = 1 \cdot (6)$

Multiply $6$ by $1$ .

$- x + 3 = 6$

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

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Subtract $3$ from both sides of the equation.

$- x = 6 - 3$

Subtract $3$ from $6$ .

$- x = 3$

Multiply each term in $- x = 3$ by $- 1$

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Multiply each term in $- x = 3$ by $- 1$ .

$(- x) \cdot - 1 = 3 \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x = 3 \cdot - 1$

Multiply $x$ by $1$ .

$x = 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$x = - 3$

Solve for x x/3-(x-1)/2=1

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