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

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

Step 1

Simplify $- \frac{1}{3} \cdot (3 x + 5)$ .

Rewrite.

$- x - 5 = 0 + 0 - \frac{1}{3} \cdot (3 x + 5)$

Simplify by adding zeros.

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

Apply the distributive property.

$- x - 5 = - \frac{1}{3} (3 x) - \frac{1}{3} \cdot 5$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$- x - 5 = \frac{- 1}{3} (3 x) - \frac{1}{3} \cdot 5$

Factor $3$ out of $3 x$ .

$- x - 5 = \frac{- 1}{3} (3 (x)) - \frac{1}{3} \cdot 5$

Cancel the common factor.

$- x - 5 = \frac{- 1}{3} (3 x) - \frac{1}{3} \cdot 5$

Rewrite the expression.

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

Multiply $- \frac{1}{3} \cdot 5$ .

Multiply $5$ by $- 1$ .

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

Combine $- 5$ and $\frac{1}{3}$ .

$- x - 5 = - 1 x + \frac{- 5}{3}$

Simplify each term.

Rewrite $- 1 x$ as $- x$ .

$- x - 5 = - x + \frac{- 5}{3}$

Move the negative in front of the fraction.

$- x - 5 = - x - \frac{5}{3}$

Step 2

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

Add $x$ to both sides of the equation.

$- x - 5 + x = - \frac{5}{3}$

Combine the opposite terms in $- x - 5 + x$ .

Add $- x$ and $x$ .

$0 - 5 = - \frac{5}{3}$

Subtract $5$ from $0$ .

$- 5 = - \frac{5}{3}$

Step 3

Since $- 5 \neq - \frac{5}{3}$ , there are no solutions.

No solution