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

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

Step 1

Rewrite the equation as $\frac{1}{2} - (x + \frac{6}{5}) = \frac{6}{5}$ .

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

Step 2

Simplify $\frac{1}{2} - (x + \frac{6}{5})$ .

Apply the distributive property.

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

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

To write $- \frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

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

Multiply $2$ by $5$ .

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

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

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

Multiply $5$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 6$ by $2$ .

$- x + \frac{5 - 12}{10} = \frac{6}{5}$

Subtract $12$ from $5$ .

$- x + \frac{- 7}{10} = \frac{6}{5}$

Move the negative in front of the fraction.

$- x - \frac{7}{10} = \frac{6}{5}$

Step 3

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

Add $\frac{7}{10}$ to both sides of the equation.

$- x = \frac{6}{5} + \frac{7}{10}$

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- x = \frac{6}{5} \cdot \frac{2}{2} + \frac{7}{10}$

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

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

$- x = \frac{6 \cdot 2}{5 \cdot 2} + \frac{7}{10}$

Multiply $5$ by $2$ .

$- x = \frac{6 \cdot 2}{10} + \frac{7}{10}$

Combine the numerators over the common denominator.

$- x = \frac{6 \cdot 2 + 7}{10}$

Simplify the numerator.

Multiply $6$ by $2$ .

$- x = \frac{12 + 7}{10}$

Add $12$ and $7$ .

$- x = \frac{19}{10}$

Step 4

Divide each term in $- x = \frac{19}{10}$ by $- 1$ and simplify.

Divide each term in $- x = \frac{19}{10}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\frac{19}{10}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\frac{19}{10}}{- 1}$

Divide $x$ by $1$ .

$x = \frac{\frac{19}{10}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{19}{10}}{- 1}$ .

$x = - 1 \cdot \frac{19}{10}$

Rewrite $- 1 \cdot \frac{19}{10}$ as $- \frac{19}{10}$ .

$x = - \frac{19}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{19}{10}$

Decimal Form:

$x = - 1.9$

Mixed Number Form:

$x = - 1 \frac{9}{10}$

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

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