Solve for x -8+1/2(-x-4)-5x=-6(-1/3x+2)

$- 8 + \frac{1}{2} (- x - 4) - 5 x = - 6 (- \frac{1}{3} x + 2)$

Step 1

Simplify $- 8 + \frac{1}{2} \cdot (- x - 4) - 5 x$ .

Simplify each term.

Apply the distributive property.

$- 8 + \frac{1}{2} (- x) + \frac{1}{2} \cdot - 4 - 5 x = - 6 (- \frac{1}{3} x + 2)$

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

$- 8 - \frac{x}{2} + \frac{1}{2} \cdot - 4 - 5 x = - 6 (- \frac{1}{3} x + 2)$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$- 8 - \frac{x}{2} + \frac{1}{2} \cdot (2 (- 2)) - 5 x = - 6 (- \frac{1}{3} x + 2)$

Cancel the common factor.

$- 8 - \frac{x}{2} + \frac{1}{2} \cdot (2 \cdot - 2) - 5 x = - 6 (- \frac{1}{3} x + 2)$

Rewrite the expression.

$- 8 - \frac{x}{2} - 2 - 5 x = - 6 (- \frac{1}{3} x + 2)$

Subtract $2$ from $- 8$ .

$- \frac{x}{2} - 10 - 5 x = - 6 (- \frac{1}{3} x + 2)$

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} - 5 x \cdot \frac{2}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Simplify terms.

Combine $- 5 x$ and $\frac{2}{2}$ .

$- \frac{x}{2} + \frac{- 5 x \cdot 2}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Combine the numerators over the common denominator.

$\frac{- x - 5 x \cdot 2}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x - 5 x \cdot 2$ .

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - 5 x \cdot 2}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Factor $x$ out of $- 5 x \cdot 2$ .

$\frac{x \cdot - 1 + x (- 5 \cdot 2)}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Factor $x$ out of $x \cdot - 1 + x (- 5 \cdot 2)$ .

$\frac{x (- 1 - 5 \cdot 2)}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Multiply $- 5$ by $2$ .

$\frac{x (- 1 - 10)}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Subtract $10$ from $- 1$ .

$\frac{x \cdot - 11}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Move $- 11$ to the left of $x$ .

$\frac{- 11 \cdot x}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Move the negative in front of the fraction.

$- \frac{11 x}{2} - 10 = - 6 (- \frac{1}{3} x + 2)$

Step 2

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

Combine $x$ and $\frac{1}{3}$ .

$- \frac{11 x}{2} - 10 = - 6 (- \frac{x}{3} + 2)$

Apply the distributive property.

$- \frac{11 x}{2} - 10 = - 6 (- \frac{x}{3}) - 6 \cdot 2$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- \frac{11 x}{2} - 10 = - 6 \frac{- x}{3} - 6 \cdot 2$

Factor $3$ out of $- 6$ .

$- \frac{11 x}{2} - 10 = 3 (- 2) \frac{- x}{3} - 6 \cdot 2$

Cancel the common factor.

$- \frac{11 x}{2} - 10 = 3 \cdot - 2 \frac{- x}{3} - 6 \cdot 2$

Rewrite the expression.

$- \frac{11 x}{2} - 10 = - 2 (- x) - 6 \cdot 2$

Multiply.

Multiply $- 1$ by $- 2$ .

$- \frac{11 x}{2} - 10 = 2 x - 6 \cdot 2$

Multiply $- 6$ by $2$ .

$- \frac{11 x}{2} - 10 = 2 x - 12$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$- \frac{11 x}{2} - 10 - 2 x = - 12$

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

$- \frac{11 x}{2} - 2 x \cdot \frac{2}{2} - 10 = - 12$

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

$- \frac{11 x}{2} + \frac{- 2 x \cdot 2}{2} - 10 = - 12$

Combine the numerators over the common denominator.

$\frac{- 11 x - 2 x \cdot 2}{2} - 10 = - 12$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 11 x - 2 x \cdot 2$ .

Factor $x$ out of $- 11 x$ .

$\frac{x \cdot - 11 - 2 x \cdot 2}{2} - 10 = - 12$

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

$\frac{x \cdot - 11 + x (- 2 \cdot 2)}{2} - 10 = - 12$

Factor $x$ out of $x \cdot - 11 + x (- 2 \cdot 2)$ .

$\frac{x (- 11 - 2 \cdot 2)}{2} - 10 = - 12$

Multiply $- 2$ by $2$ .

$\frac{x (- 11 - 4)}{2} - 10 = - 12$

Subtract $4$ from $- 11$ .

$\frac{x \cdot - 15}{2} - 10 = - 12$

Move $- 15$ to the left of $x$ .

$\frac{- 15 \cdot x}{2} - 10 = - 12$

Move the negative in front of the fraction.

$- \frac{15 x}{2} - 10 = - 12$

Step 4

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

Add $10$ to both sides of the equation.

$- \frac{15 x}{2} = - 12 + 10$

Add $- 12$ and $10$ .

$- \frac{15 x}{2} = - 2$

Step 5

Multiply both sides of the equation by $- \frac{2}{15}$ .

$- \frac{2}{15} (- \frac{15 x}{2}) = - \frac{2}{15} \cdot - 2$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{15} (- \frac{15 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{15}$ into the numerator.

$\frac{- 2}{15} (- \frac{15 x}{2}) = - \frac{2}{15} \cdot - 2$

Move the leading negative in $- \frac{15 x}{2}$ into the numerator.

$\frac{- 2}{15} \cdot \frac{- 15 x}{2} = - \frac{2}{15} \cdot - 2$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{15} \cdot \frac{- 15 x}{2} = - \frac{2}{15} \cdot - 2$

Cancel the common factor.

$\frac{2 \cdot - 1}{15} \cdot \frac{- 15 x}{2} = - \frac{2}{15} \cdot - 2$

Rewrite the expression.

$\frac{- 1}{15} (- 15 x) = - \frac{2}{15} \cdot - 2$

Cancel the common factor of $15$ .

Factor $15$ out of $- 15 x$ .

$\frac{- 1}{15} (15 (- x)) = - \frac{2}{15} \cdot - 2$

Cancel the common factor.

$\frac{- 1}{15} (15 (- x)) = - \frac{2}{15} \cdot - 2$

Rewrite the expression.

$- - x = - \frac{2}{15} \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{15} \cdot - 2$

Multiply $x$ by $1$ .

$x = - \frac{2}{15} \cdot - 2$

Simplify the right side.

Multiply $- \frac{2}{15} \cdot - 2$ .

Multiply $- 2$ by $- 1$ .

$x = 2 (\frac{2}{15})$

Combine $2$ and $\frac{2}{15}$ .

$x = \frac{2 \cdot 2}{15}$

Multiply $2$ by $2$ .

$x = \frac{4}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{15}$

Decimal Form:

$x = 0.2\overline{6}$

Solve for x -8+1/2(-x-4)-5x=-6(-1/3x+2)

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