Solve for x 1-(x-3)/2=(2-x)/3+4

$1 - \frac{x - 3}{2} = \frac{2 - x}{3} + 4$

Step 1

Simplify $1 - \frac{x - 3}{2}$ .

Combine into one fraction.

Write $1$ as a fraction with a common denominator.

$\frac{2}{2} - \frac{x - 3}{2} = \frac{2 - x}{3} + 4$

Combine the numerators over the common denominator.

$\frac{2 - (x - 3)}{2} = \frac{2 - x}{3} + 4$

Simplify the numerator.

Apply the distributive property.

$\frac{2 - x - - 3}{2} = \frac{2 - x}{3} + 4$

Multiply $- 1$ by $- 3$ .

$\frac{2 - x + 3}{2} = \frac{2 - x}{3} + 4$

Add $2$ and $3$ .

$\frac{- x + 5}{2} = \frac{2 - x}{3} + 4$

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

$\frac{- (x) + 5}{2} = \frac{2 - x}{3} + 4$

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{- (x) - 1 (- 5)}{2} = \frac{2 - x}{3} + 4$

Factor $- 1$ out of $- (x) - 1 (- 5)$ .

$\frac{- (x - 5)}{2} = \frac{2 - x}{3} + 4$

Simplify the expression.

Rewrite $- (x - 5)$ as $- 1 (x - 5)$ .

$\frac{- 1 (x - 5)}{2} = \frac{2 - x}{3} + 4$

Move the negative in front of the fraction.

$- \frac{x - 5}{2} = \frac{2 - x}{3} + 4$

Step 2

Simplify $\frac{2 - x}{3} + 4$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x - 5}{2} = \frac{2 - x}{3} + 4 \cdot \frac{3}{3}$

Simplify terms.

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

$- \frac{x - 5}{2} = \frac{2 - x}{3} + \frac{4 \cdot 3}{3}$

Combine the numerators over the common denominator.

$- \frac{x - 5}{2} = \frac{2 - x + 4 \cdot 3}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$- \frac{x - 5}{2} = \frac{2 - x + 12}{3}$

Add $2$ and $12$ .

$- \frac{x - 5}{2} = \frac{- x + 14}{3}$

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

$- \frac{x - 5}{2} = \frac{- (x) + 14}{3}$

Rewrite $14$ as $- 1 (- 14)$ .

$- \frac{x - 5}{2} = \frac{- (x) - 1 (- 14)}{3}$

Factor $- 1$ out of $- (x) - 1 (- 14)$ .

$- \frac{x - 5}{2} = \frac{- (x - 14)}{3}$

Simplify the expression.

Rewrite $- (x - 14)$ as $- 1 (x - 14)$ .

$- \frac{x - 5}{2} = \frac{- 1 (x - 14)}{3}$

Move the negative in front of the fraction.

$- \frac{x - 5}{2} = - \frac{x - 14}{3}$

Step 3

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

Add $\frac{x - 14}{3}$ to both sides of the equation.

$- \frac{x - 5}{2} + \frac{x - 14}{3} = 0$

To write $- \frac{x - 5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x - 5}{2} \cdot \frac{3}{3} + \frac{x - 14}{3} = 0$

To write $\frac{x - 14}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x - 5}{2} \cdot \frac{3}{3} + \frac{x - 14}{3} \cdot \frac{2}{2} = 0$

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

Multiply $\frac{x - 5}{2}$ by $\frac{3}{3}$ .

$- \frac{(x - 5) \cdot 3}{2 \cdot 3} + \frac{x - 14}{3} \cdot \frac{2}{2} = 0$

Multiply $2$ by $3$ .

$- \frac{(x - 5) \cdot 3}{6} + \frac{x - 14}{3} \cdot \frac{2}{2} = 0$

Multiply $\frac{x - 14}{3}$ by $\frac{2}{2}$ .

$- \frac{(x - 5) \cdot 3}{6} + \frac{(x - 14) \cdot 2}{3 \cdot 2} = 0$

Multiply $3$ by $2$ .

$- \frac{(x - 5) \cdot 3}{6} + \frac{(x - 14) \cdot 2}{6} = 0$

Combine the numerators over the common denominator.

$\frac{- (x - 5) \cdot 3 + (x - 14) \cdot 2}{6} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{(- x - - 5) \cdot 3 + (x - 14) \cdot 2}{6} = 0$

Multiply $- 1$ by $- 5$ .

$\frac{(- x + 5) \cdot 3 + (x - 14) \cdot 2}{6} = 0$

Apply the distributive property.

$\frac{- x \cdot 3 + 5 \cdot 3 + (x - 14) \cdot 2}{6} = 0$

Multiply $3$ by $- 1$ .

$\frac{- 3 x + 5 \cdot 3 + (x - 14) \cdot 2}{6} = 0$

Multiply $5$ by $3$ .

$\frac{- 3 x + 15 + (x - 14) \cdot 2}{6} = 0$

Apply the distributive property.

$\frac{- 3 x + 15 + x \cdot 2 - 14 \cdot 2}{6} = 0$

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

$\frac{- 3 x + 15 + 2 \cdot x - 14 \cdot 2}{6} = 0$

Multiply $- 14$ by $2$ .

$\frac{- 3 x + 15 + 2 \cdot x - 28}{6} = 0$

Add $- 3 x$ and $2 x$ .

$\frac{- x + 15 - 28}{6} = 0$

Subtract $28$ from $15$ .

$\frac{- x - 13}{6} = 0$

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 13}{6} = 0$

Rewrite $- 13$ as $- 1 (13)$ .

$\frac{- (x) - 1 (13)}{6} = 0$

Factor $- 1$ out of $- (x) - 1 (13)$ .

$\frac{- (x + 13)}{6} = 0$

Rewrite $- (x + 13)$ as $- 1 (x + 13)$ .

$\frac{- 1 (x + 13)}{6} = 0$

Move the negative in front of the fraction.

$- \frac{x + 13}{6} = 0$

Step 4

Set the numerator equal to zero.

$x + 13 = 0$

Step 5

Subtract $13$ from both sides of the equation.

$x = - 13$

Solve for x 1-(x-3)/2=(2-x)/3+4

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