Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

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

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

Step 1.4.2

Factor $3$ out of $3 x$ .

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

Step 1.4.3

Cancel the common factor.

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

Step 1.4.4

Rewrite the expression.

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

Step 1.5

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

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Step 1.5.1

Multiply $5$ by $- 1$ .

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

Step 1.5.2

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

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

Step 1.6

Simplify each term.

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Step 1.6.1

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

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

Step 1.6.2

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.

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Step 2.1

Add $x$ to both sides of the equation.

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

Step 2.2

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

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Step 2.2.1

Add $- x$ and $x$ .

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

Step 2.2.2

Subtract $5$ from $0$ .

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

Step 3

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

No solution