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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $2$ .

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

Add $- 2$ and $1$ .

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

Move the negative in front of the fraction.

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

Step 2

Simplify $4 + \frac{1}{2} \cdot (- 9 x + 2)$ .

Simplify each term.

Apply the distributive property.

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

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

Combine $- 9$ and $\frac{1}{2}$ .

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

Combine $\frac{- 9}{2}$ and $x$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Add $4$ and $1$ .

$x - \frac{1}{2} = - \frac{9 x}{2} + 5$

Step 3

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

Add $\frac{9 x}{2}$ to both sides of the equation.

$x - \frac{1}{2} + \frac{9 x}{2} = 5$

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

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

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

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

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

$\frac{2 x + 9 x - 1}{2} = 5$

Add $2 x$ and $9 x$ .

$\frac{11 x - 1}{2} = 5$

Step 4

Multiply both sides by $2$ .

$\frac{11 x - 1}{2} \cdot 2 = 5 \cdot 2$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{11 x - 1}{2} \cdot 2 = 5 \cdot 2$

Rewrite the expression.

$11 x - 1 = 5 \cdot 2$

Simplify the right side.

Multiply $5$ by $2$ .

$11 x - 1 = 10$

Step 6

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$11 x = 10 + 1$

Add $10$ and $1$ .

$11 x = 11$

Divide each term in $11 x = 11$ by $11$ and simplify.

Divide each term in $11 x = 11$ by $11$ .

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

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $11$ by $11$ .

$x = 1$

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

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