Solve for x -(1/2x+9)=-3x-4(x-1/2)+1

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Simplify $- 3 x - 4 (x - \frac{1}{2}) + 1$ .

Simplify each term.

Apply the distributive property.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 2$ by $- 1$ .

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

Simplify by adding terms.

Subtract $4 x$ from $- 3 x$ .

$- 7 x + 2 + 1 = - (\frac{1}{2} x + 9)$

Add $2$ and $1$ .

$- 7 x + 3 = - (\frac{1}{2} x + 9)$

Simplify $- (\frac{1}{2} x + 9)$ .

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

$- 7 x + 3 = - (\frac{x}{2} + 9)$

Apply the distributive property.

$- 7 x + 3 = - \frac{x}{2} - 1 \cdot 9$

Multiply $- 1$ by $9$ .

$- 7 x + 3 = - \frac{x}{2} - 9$

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

Add $\frac{x}{2}$ to both sides of the equation.

$- 7 x + 3 + \frac{x}{2} = - 9$

To write $- 7 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 7 x \cdot \frac{2}{2} + \frac{x}{2} + 3 = - 9$

Combine $- 7 x$ and $\frac{2}{2}$ .

$\frac{- 7 x \cdot 2}{2} + \frac{x}{2} + 3 = - 9$

Combine the numerators over the common denominator.

$\frac{- 7 x \cdot 2 + x}{2} + 3 = - 9$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 7 x \cdot 2 + x$ .

Factor $x$ out of $- 7 x \cdot 2$ .

$\frac{x (- 7 \cdot 2) + x}{2} + 3 = - 9$

Raise $x$ to the power of $1$ .

$\frac{x (- 7 \cdot 2) + x^{1}}{2} + 3 = - 9$

Factor $x$ out of $x^{1}$ .

$\frac{x (- 7 \cdot 2) + x \cdot 1}{2} + 3 = - 9$

Factor $x$ out of $x (- 7 \cdot 2) + x \cdot 1$ .

$\frac{x (- 7 \cdot 2 + 1)}{2} + 3 = - 9$

Multiply $- 7$ by $2$ .

$\frac{x (- 14 + 1)}{2} + 3 = - 9$

Add $- 14$ and $1$ .

$\frac{x \cdot - 13}{2} + 3 = - 9$

Move $- 13$ to the left of $x$ .

$\frac{- 13 \cdot x}{2} + 3 = - 9$

Move the negative in front of the fraction.

$- \frac{13 x}{2} + 3 = - 9$

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

Subtract $3$ from both sides of the equation.

$- \frac{13 x}{2} = - 9 - 3$

Subtract $3$ from $- 9$ .

$- \frac{13 x}{2} = - 12$

Multiply both sides of the equation by $- \frac{2}{13}$ .

$- \frac{2}{13} (- \frac{13 x}{2}) = - \frac{2}{13} \cdot - 12$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{13} (- \frac{13 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{13}$ into the numerator.

$\frac{- 2}{13} (- \frac{13 x}{2}) = - \frac{2}{13} \cdot - 12$

Move the leading negative in $- \frac{13 x}{2}$ into the numerator.

$\frac{- 2}{13} \cdot \frac{- 13 x}{2} = - \frac{2}{13} \cdot - 12$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{13} \cdot \frac{- 13 x}{2} = - \frac{2}{13} \cdot - 12$

Cancel the common factor.

$\frac{2 \cdot - 1}{13} \cdot \frac{- 13 x}{2} = - \frac{2}{13} \cdot - 12$

Rewrite the expression.

$\frac{- 1}{13} (- 13 x) = - \frac{2}{13} \cdot - 12$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 x$ .

$\frac{- 1}{13} (13 (- x)) = - \frac{2}{13} \cdot - 12$

Cancel the common factor.

$\frac{- 1}{13} (13 (- x)) = - \frac{2}{13} \cdot - 12$

Rewrite the expression.

$- - x = - \frac{2}{13} \cdot - 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{13} \cdot - 12$

Multiply $x$ by $1$ .

$x = - \frac{2}{13} \cdot - 12$

Simplify the right side.

Multiply $- \frac{2}{13} \cdot - 12$ .

Multiply $- 12$ by $- 1$ .

$x = 12 (\frac{2}{13})$

Combine $12$ and $\frac{2}{13}$ .

$x = \frac{12 \cdot 2}{13}$

Multiply $12$ by $2$ .

$x = \frac{24}{13}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{13}$

Decimal Form:

$x = 1.\overline{846153}$

Mixed Number Form:

$x = 1 \frac{11}{13}$

Solve for x -(1/2x+9)=-3x-4(x-1/2)+1

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