Solve for x 1/2(-x+8)-9x=-6+5/2(-x+6)

$\frac{1}{2} (- x + 8) - 9 x = - 6 + \frac{5}{2} (- x + 6)$

Step 1

Simplify $\frac{1}{2} \cdot (- x + 8) - 9 x$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} (- x) + \frac{1}{2} \cdot 8 - 9 x = - 6 + \frac{5}{2} \cdot (- x + 6)$

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

$- \frac{x}{2} + \frac{1}{2} \cdot 8 - 9 x = - 6 + \frac{5}{2} \cdot (- x + 6)$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$- \frac{x}{2} + \frac{1}{2} \cdot (2 (4)) - 9 x = - 6 + \frac{5}{2} \cdot (- x + 6)$

Cancel the common factor.

$- \frac{x}{2} + \frac{1}{2} \cdot (2 \cdot 4) - 9 x = - 6 + \frac{5}{2} \cdot (- x + 6)$

Rewrite the expression.

$- \frac{x}{2} + 4 - 9 x = - 6 + \frac{5}{2} \cdot (- x + 6)$

To write $- 9 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} - 9 x \cdot \frac{2}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Simplify terms.

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

$- \frac{x}{2} + \frac{- 9 x \cdot 2}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Combine the numerators over the common denominator.

$\frac{- x - 9 x \cdot 2}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x - 9 x \cdot 2$ .

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - 9 x \cdot 2}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Factor $x$ out of $- 9 x \cdot 2$ .

$\frac{x \cdot - 1 + x (- 9 \cdot 2)}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Factor $x$ out of $x \cdot - 1 + x (- 9 \cdot 2)$ .

$\frac{x (- 1 - 9 \cdot 2)}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Multiply $- 9$ by $2$ .

$\frac{x (- 1 - 18)}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Subtract $18$ from $- 1$ .

$\frac{x \cdot - 19}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Move $- 19$ to the left of $x$ .

$\frac{- 19 \cdot x}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Move the negative in front of the fraction.

$- \frac{19 x}{2} + 4 = - 6 + \frac{5}{2} \cdot (- x + 6)$

Step 2

Simplify $- 6 + \frac{5}{2} \cdot (- x + 6)$ .

Simplify each term.

Apply the distributive property.

$- \frac{19 x}{2} + 4 = - 6 + \frac{5}{2} (- x) + \frac{5}{2} \cdot 6$

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

$- \frac{19 x}{2} + 4 = - 6 - \frac{5 x}{2} + \frac{5}{2} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$- \frac{19 x}{2} + 4 = - 6 - \frac{5 x}{2} + \frac{5}{2} \cdot (2 (3))$

Cancel the common factor.

$- \frac{19 x}{2} + 4 = - 6 - \frac{5 x}{2} + \frac{5}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$- \frac{19 x}{2} + 4 = - 6 - \frac{5 x}{2} + 5 \cdot 3$

Multiply $5$ by $3$ .

$- \frac{19 x}{2} + 4 = - 6 - \frac{5 x}{2} + 15$

Add $- 6$ and $15$ .

$- \frac{19 x}{2} + 4 = - \frac{5 x}{2} + 9$

Step 3

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

Add $\frac{5 x}{2}$ to both sides of the equation.

$- \frac{19 x}{2} + 4 + \frac{5 x}{2} = 9$

Combine the numerators over the common denominator.

$4 + \frac{- 19 x + 5 x}{2} = 9$

Add $- 19 x$ and $5 x$ .

$4 + \frac{- 14 x}{2} = 9$

Cancel the common factor of $- 14$ and $2$ .

Factor $2$ out of $- 14 x$ .

$4 + \frac{2 (- 7 x)}{2} = 9$

Cancel the common factors.

Factor $2$ out of $2$ .

$4 + \frac{2 (- 7 x)}{2 (1)} = 9$

Cancel the common factor.

$4 + \frac{2 (- 7 x)}{2 \cdot 1} = 9$

Rewrite the expression.

$4 + \frac{- 7 x}{1} = 9$

Divide $- 7 x$ by $1$ .

$4 - 7 x = 9$

Step 4

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

Subtract $4$ from both sides of the equation.

$- 7 x = 9 - 4$

Subtract $4$ from $9$ .

$- 7 x = 5$

Step 5

Divide each term in $- 7 x = 5$ by $- 7$ and simplify.

Divide each term in $- 7 x = 5$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{5}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{5}{- 7}$

Divide $x$ by $1$ .

$x = \frac{5}{- 7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{7}$

Decimal Form:

$x = - 0.\overline{714285}$

Solve for x 1/2(-x+8)-9x=-6+5/2(-x+6)

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