Solve for x -(1/2x+3)-3=-9-1/5x

$- (\frac{1}{2} x + 3) - 3 = - 9 - \frac{1}{5} x$

Step 1

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

Simplify each term.

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

$- (\frac{x}{2} + 3) - 3 = - 9 - \frac{1}{5} x$

Apply the distributive property.

$- \frac{x}{2} - 1 \cdot 3 - 3 = - 9 - \frac{1}{5} x$

Multiply $- 1$ by $3$ .

$- \frac{x}{2} - 3 - 3 = - 9 - \frac{1}{5} x$

Subtract $3$ from $- 3$ .

$- \frac{x}{2} - 6 = - 9 - \frac{1}{5} x$

Step 2

Combine $x$ and $\frac{1}{5}$ .

$- \frac{x}{2} - 6 = - 9 - \frac{x}{5}$

Step 3

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

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

$- \frac{x}{2} - 6 + \frac{x}{5} = - 9$

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

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

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

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

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{5}{5}$ .

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

Multiply $2$ by $5$ .

$- \frac{x \cdot 5}{10} + \frac{x}{5} \cdot \frac{2}{2} - 6 = - 9$

Multiply $\frac{x}{5}$ by $\frac{2}{2}$ .

$- \frac{x \cdot 5}{10} + \frac{x \cdot 2}{5 \cdot 2} - 6 = - 9$

Multiply $5$ by $2$ .

$- \frac{x \cdot 5}{10} + \frac{x \cdot 2}{10} - 6 = - 9$

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 + x \cdot 2}{10} - 6 = - 9$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x (- 1 \cdot 5) + x \cdot 2}{10} - 6 = - 9$

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

$\frac{x (- 1 \cdot 5) + x (2)}{10} - 6 = - 9$

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

$\frac{x (- 1 \cdot 5 + 2)}{10} - 6 = - 9$

Multiply $- 1$ by $5$ .

$\frac{x (- 5 + 2)}{10} - 6 = - 9$

Add $- 5$ and $2$ .

$\frac{x \cdot - 3}{10} - 6 = - 9$

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{10} - 6 = - 9$

Move the negative in front of the fraction.

$- \frac{3 x}{10} - 6 = - 9$

Step 4

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

Add $6$ to both sides of the equation.

$- \frac{3 x}{10} = - 9 + 6$

Add $- 9$ and $6$ .

$- \frac{3 x}{10} = - 3$

Step 5

Multiply both sides of the equation by $- \frac{10}{3}$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{10}{3} (- \frac{3 x}{10})$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{10}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 x}{10}$ into the numerator.

$\frac{- 10}{3} \cdot \frac{- 3 x}{10} = - \frac{10}{3} \cdot - 3$

Factor $10$ out of $- 10$ .

$\frac{10 (- 1)}{3} \cdot \frac{- 3 x}{10} = - \frac{10}{3} \cdot - 3$

Cancel the common factor.

$\frac{10 \cdot - 1}{3} \cdot \frac{- 3 x}{10} = - \frac{10}{3} \cdot - 3$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{10}{3} \cdot - 3$

Cancel the common factor of $3$ .

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

$\frac{- 1}{3} (3 (- x)) = - \frac{10}{3} \cdot - 3$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{10}{3} \cdot - 3$

Rewrite the expression.

$- - x = - \frac{10}{3} \cdot - 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{10}{3} \cdot - 3$

Multiply $x$ by $1$ .

$x = - \frac{10}{3} \cdot - 3$

Simplify the right side.

Simplify $- \frac{10}{3} \cdot - 3$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$x = \frac{- 10}{3} \cdot - 3$

Factor $3$ out of $- 3$ .

$x = \frac{- 10}{3} \cdot (3 (- 1))$

Cancel the common factor.

$x = \frac{- 10}{3} \cdot (3 \cdot - 1)$

Rewrite the expression.

$x = - 10 \cdot - 1$

Multiply $- 10$ by $- 1$ .

$x = 10$

Solve for x -(1/2x+3)-3=-9-1/5x

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