Solve for x -1/2+2/3(-6x-6)=-4

$- \frac{1}{2} + \frac{2}{3} (- 6 x - 6) = - 4$

Step 1

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

Simplify each term.

Apply the distributive property.

$- \frac{1}{2} + \frac{2}{3} (- 6 x) + \frac{2}{3} \cdot - 6 = - 4$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6 x$ .

$- \frac{1}{2} + \frac{2}{3} (3 (- 2 x)) + \frac{2}{3} \cdot - 6 = - 4$

Cancel the common factor.

$- \frac{1}{2} + \frac{2}{3} (3 (- 2 x)) + \frac{2}{3} \cdot - 6 = - 4$

Rewrite the expression.

$- \frac{1}{2} + 2 (- 2 x) + \frac{2}{3} \cdot - 6 = - 4$

Multiply $- 2$ by $2$ .

$- \frac{1}{2} - 4 x + \frac{2}{3} \cdot - 6 = - 4$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 2$ .

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

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 4$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $2$ .

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

Subtract $8$ from $- 1$ .

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

Move the negative in front of the fraction.

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

Step 2

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

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

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

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 4$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $2$ .

$- 4 x = \frac{- 8 + 9}{2}$

Add $- 8$ and $9$ .

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

Step 3

Divide each term in $- 4 x = \frac{1}{2}$ by $- 4$ and simplify.

Divide each term in $- 4 x = \frac{1}{2}$ by $- 4$ .

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Move the negative in front of the fraction.

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

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

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

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

Multiply $2$ by $4$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.125$

Solve for x -1/2+2/3(-6x-6)=-4

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