Solve for x 2x-1-(3x+3)/2=(2x-5)/14

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

Multiply both sides by $14$ .

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

Simplify.

Simplify the left side.

Simplify $(2 x - 1 - \frac{3 x + 3}{2}) \cdot 14$ .

Factor $3$ out of $3 x + 3$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $3$ .

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

Factor $3$ out of $3 (x) + 3 (1)$ .

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

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

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

Simplify terms.

Combine $2 x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

$(\frac{4 x - 3 (x + 1)}{2} - 1) \cdot 14 = \frac{2 x - 5}{14} \cdot 14$

Apply the distributive property.

$(\frac{4 x - 3 x - 3 \cdot 1}{2} - 1) \cdot 14 = \frac{2 x - 5}{14} \cdot 14$

Multiply $- 3$ by $1$ .

$(\frac{4 x - 3 x - 3}{2} - 1) \cdot 14 = \frac{2 x - 5}{14} \cdot 14$

Subtract $3 x$ from $4 x$ .

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

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

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

Simplify terms.

Combine $- 1$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $- 3$ .

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

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

$\frac{x - 5}{2} \cdot (2 (7)) = \frac{2 x - 5}{14} \cdot 14$

Cancel the common factor.

$\frac{x - 5}{2} \cdot (2 \cdot 7) = \frac{2 x - 5}{14} \cdot 14$

Rewrite the expression.

$(x - 5) \cdot 7 = \frac{2 x - 5}{14} \cdot 14$

Apply the distributive property.

$x \cdot 7 - 5 \cdot 7 = \frac{2 x - 5}{14} \cdot 14$

Simplify the expression.

Move $7$ to the left of $x$ .

$7 \cdot x - 5 \cdot 7 = \frac{2 x - 5}{14} \cdot 14$

Multiply $- 5$ by $7$ .

$7 x - 35 = \frac{2 x - 5}{14} \cdot 14$

Simplify the right side.

Cancel the common factor of $14$ .

Cancel the common factor.

$7 x - 35 = \frac{2 x - 5}{14} \cdot 14$

Rewrite the expression.

$7 x - 35 = 2 x - 5$

Solve for $x$ .

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

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

$7 x - 35 - 2 x = - 5$

Subtract $2 x$ from $7 x$ .

$5 x - 35 = - 5$

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

Add $35$ to both sides of the equation.

$5 x = - 5 + 35$

Add $- 5$ and $35$ .

$5 x = 30$

Divide each term in $5 x = 30$ by $5$ and simplify.

Divide each term in $5 x = 30$ by $5$ .

$\frac{5 x}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{30}{5}$

Divide $x$ by $1$ .

$x = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$

Solve for x 2x-1-(3x+3)/2=(2x-5)/14

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