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

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $- - \frac{1}{2}$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{1}{2}$ by $1$ .

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

Simplify the expression.

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $2$ .

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

Simplify $2 (\frac{3}{2} x - 6) + 1$ .

Simplify each term.

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 6$ .

$- x + \frac{3}{2} = 3 x - 12 + 1$

Add $- 12$ and $1$ .

$- x + \frac{3}{2} = 3 x - 11$

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

Subtract $3 x$ from both sides of the equation.

$- x + \frac{3}{2} - 3 x = - 11$

Subtract $3 x$ from $- x$ .

$- 4 x + \frac{3}{2} = - 11$

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

Subtract $\frac{3}{2}$ from both sides of the equation.

$- 4 x = - 11 - \frac{3}{2}$

To write $- 11$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 4 x = - 11 \cdot \frac{2}{2} - \frac{3}{2}$

Combine $- 11$ and $\frac{2}{2}$ .

$- 4 x = \frac{- 11 \cdot 2}{2} - \frac{3}{2}$

Combine the numerators over the common denominator.

$- 4 x = \frac{- 11 \cdot 2 - 3}{2}$

Simplify the numerator.

Multiply $- 11$ by $2$ .

$- 4 x = \frac{- 22 - 3}{2}$

Subtract $3$ from $- 22$ .

$- 4 x = \frac{- 25}{2}$

Move the negative in front of the fraction.

$- 4 x = - \frac{25}{2}$

Divide each term in $- 4 x = - \frac{25}{2}$ by $- 4$ and simplify.

Divide each term in $- 4 x = - \frac{25}{2}$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- \frac{25}{2}}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- \frac{25}{2}}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- \frac{25}{2}}{- 4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{25}{2} \cdot \frac{1}{- 4}$

Move the negative in front of the fraction.

$x = - \frac{25}{2} (- \frac{1}{4})$

Multiply $- \frac{25}{2} (- \frac{1}{4})$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{25}{2}) \frac{1}{4}$

Multiply $\frac{25}{2}$ by $1$ .

$x = \frac{25}{2} \cdot \frac{1}{4}$

Multiply $\frac{25}{2}$ by $\frac{1}{4}$ .

$x = \frac{25}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{25}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{8}$

Decimal Form:

$x = 3.125$

Mixed Number Form:

$x = 3 \frac{1}{8}$

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

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