Solve for x -2x+4(-1/4x+7/2)=-(x-1)-8x

$- 2 x + 4 (- \frac{1}{4} x + \frac{7}{2}) = - (x - 1) - 8 x$

Simplify $- 2 x + 4 (- \frac{1}{4} x + \frac{7}{2})$ .

Simplify each term.

Combine $x$ and $\frac{1}{4}$ .

$- 2 x + 4 (- \frac{x}{4} + \frac{7}{2}) = - (x - 1) - 8 x$

Apply the distributive property.

$- 2 x + 4 (- \frac{x}{4}) + 4 (\frac{7}{2}) = - (x - 1) - 8 x$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$- 2 x + 4 \frac{- x}{4} + 4 (\frac{7}{2}) = - (x - 1) - 8 x$

Cancel the common factor.

$- 2 x + 4 \frac{- x}{4} + 4 (\frac{7}{2}) = - (x - 1) - 8 x$

Rewrite the expression.

$- 2 x - x + 4 (\frac{7}{2}) = - (x - 1) - 8 x$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$- 2 x - x + 2 (2) \frac{7}{2} = - (x - 1) - 8 x$

Cancel the common factor.

$- 2 x - x + 2 \cdot 2 \frac{7}{2} = - (x - 1) - 8 x$

Rewrite the expression.

$- 2 x - x + 2 \cdot 7 = - (x - 1) - 8 x$

Multiply $2$ by $7$ .

$- 2 x - x + 14 = - (x - 1) - 8 x$

Subtract $x$ from $- 2 x$ .

$- 3 x + 14 = - (x - 1) - 8 x$

Simplify $- (x - 1) - 8 x$ .

Simplify each term.

Apply the distributive property.

$- 3 x + 14 = - x - - 1 - 8 x$

Multiply $- 1$ by $- 1$ .

$- 3 x + 14 = - x + 1 - 8 x$

Subtract $8 x$ from $- x$ .

$- 3 x + 14 = - 9 x + 1$

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

Add $9 x$ to both sides of the equation.

$- 3 x + 14 + 9 x = 1$

Add $- 3 x$ and $9 x$ .

$6 x + 14 = 1$

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

Subtract $14$ from both sides of the equation.

$6 x = 1 - 14$

Subtract $14$ from $1$ .

$6 x = - 13$

Divide each term in $6 x = - 13$ by $6$ and simplify.

Divide each term in $6 x = - 13$ by $6$ .

$\frac{6 x}{6} = \frac{- 13}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 13}{6}$

Divide $x$ by $1$ .

$x = \frac{- 13}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{13}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{6}$

Decimal Form:

$x = - 2.1\overline{6}$

Mixed Number Form:

$x = - 2 \frac{1}{6}$

Solve for x -2x+4(-1/4x+7/2)=-(x-1)-8x

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