Solve for x (3x-2)/4-(2x-5)/3=(1+x)/6

$\frac{3 x - 2}{4} - \frac{2 x - 5}{3} = \frac{1 + x}{6}$

Step 1

Multiply both sides by $6$ .

$(\frac{3 x - 2}{4} - \frac{2 x - 5}{3}) \cdot 6 = \frac{1 + x}{6} \cdot 6$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{3 x - 2}{4} - \frac{2 x - 5}{3}) \cdot 6$ .

To write $\frac{3 x - 2}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{3 x - 2}{4} \cdot \frac{3}{3} - \frac{2 x - 5}{3}) \cdot 6 = \frac{1 + x}{6} \cdot 6$

To write $- \frac{2 x - 5}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3 x - 2}{4} \cdot \frac{3}{3} - \frac{2 x - 5}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{1 + x}{6} \cdot 6$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x - 2}{4}$ by $\frac{3}{3}$ .

$(\frac{(3 x - 2) \cdot 3}{4 \cdot 3} - \frac{2 x - 5}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $4$ by $3$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{2 x - 5}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $\frac{2 x - 5}{3}$ by $\frac{4}{4}$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{(2 x - 5) \cdot 4}{3 \cdot 4}) \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $3$ by $4$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{(2 x - 5) \cdot 4}{12}) \cdot 6 = \frac{1 + x}{6} \cdot 6$

Combine the numerators over the common denominator.

$\frac{(3 x - 2) \cdot 3 - (2 x - 5) \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot 3 - 2 \cdot 3 - (2 x - 5) \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $3$ by $3$ .

$\frac{9 x - 2 \cdot 3 - (2 x - 5) \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $- 2$ by $3$ .

$\frac{9 x - 6 - (2 x - 5) \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Apply the distributive property.

$\frac{9 x - 6 + (- (2 x) - - 5) \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $2$ by $- 1$ .

$\frac{9 x - 6 + (- 2 x - - 5) \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $- 1$ by $- 5$ .

$\frac{9 x - 6 + (- 2 x + 5) \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Apply the distributive property.

$\frac{9 x - 6 - 2 x \cdot 4 + 5 \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $4$ by $- 2$ .

$\frac{9 x - 6 - 8 x + 5 \cdot 4}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Multiply $5$ by $4$ .

$\frac{9 x - 6 - 8 x + 20}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Subtract $8 x$ from $9 x$ .

$\frac{x - 6 + 20}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Add $- 6$ and $20$ .

$\frac{x + 14}{12} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{x + 14}{6 (2)} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Cancel the common factor.

$\frac{x + 14}{6 \cdot 2} \cdot 6 = \frac{1 + x}{6} \cdot 6$

Rewrite the expression.

$\frac{x + 14}{2} = \frac{1 + x}{6} \cdot 6$

Simplify the right side.

Simplify $\frac{1 + x}{6} \cdot 6$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{x + 14}{2} = \frac{1 + x}{6} \cdot 6$

Rewrite the expression.

$\frac{x + 14}{2} = 1 + x$

Reorder $1$ and $x$ .

$\frac{x + 14}{2} = x + 1$

Step 3

Solve for $x$ .

Multiply both sides by $2$ .

$\frac{x + 14}{2} \cdot 2 = (x + 1) \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x + 14}{2} \cdot 2 = (x + 1) \cdot 2$

Rewrite the expression.

$x + 14 = (x + 1) \cdot 2$

Simplify the right side.

Simplify $(x + 1) \cdot 2$ .

Apply the distributive property.

$x + 14 = x \cdot 2 + 1 \cdot 2$

Simplify the expression.

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

$x + 14 = 2 \cdot x + 1 \cdot 2$

Multiply $2$ by $1$ .

$x + 14 = 2 x + 2$

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$x + 14 - 2 x = 2$

Subtract $2 x$ from $x$ .

$- x + 14 = 2$

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

Subtract $14$ from both sides of the equation.

$- x = 2 - 14$

Subtract $14$ from $2$ .

$- x = - 12$

Divide each term in $- x = - 12$ by $- 1$ and simplify.

Divide each term in $- x = - 12$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 12}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 12}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 1}$

Simplify the right side.

Divide $- 12$ by $- 1$ .

$x = 12$

Solve for x (3x-2)/4-(2x-5)/3=(1+x)/6

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