Algebra Examples

$- \frac{1}{5} (10 - 20 u) - u = \frac{1}{3} (6 u - 12)$

Step 1

Simplify $- \frac{1}{5} \cdot (10 - 20 u) - u$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- \frac{1}{5} \cdot 10 - \frac{1}{5} (- 20 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.2

Cancel the common factor of $5$ .

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Step 1.1.2.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{- 1}{5} \cdot 10 - \frac{1}{5} (- 20 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.2.2

Factor $5$ out of $10$ .

$\frac{- 1}{5} \cdot (5 (2)) - \frac{1}{5} (- 20 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.2.3

Cancel the common factor.

$\frac{- 1}{5} \cdot (5 \cdot 2) - \frac{1}{5} (- 20 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.2.4

Rewrite the expression.

$- 1 \cdot 2 - \frac{1}{5} (- 20 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.3

Multiply $- 1$ by $2$ .

$- 2 - \frac{1}{5} (- 20 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.4

Cancel the common factor of $5$ .

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Step 1.1.4.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$- 2 + \frac{- 1}{5} (- 20 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.4.2

Factor $5$ out of $- 20 u$ .

$- 2 + \frac{- 1}{5} (5 (- 4 u)) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.4.3

Cancel the common factor.

$- 2 + \frac{- 1}{5} (5 (- 4 u)) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.4.4

Rewrite the expression.

$- 2 - 1 (- 4 u) - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.1.5

Multiply $- 4$ by $- 1$ .

$- 2 + 4 u - u = \frac{1}{3} \cdot (6 u - 12)$

Step 1.2

Subtract $u$ from $4 u$ .

$- 2 + 3 u = \frac{1}{3} \cdot (6 u - 12)$

Step 2

Simplify $\frac{1}{3} \cdot (6 u - 12)$ .

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Step 2.1

Apply the distributive property.

$- 2 + 3 u = \frac{1}{3} (6 u) + \frac{1}{3} \cdot - 12$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $6 u$ .

$- 2 + 3 u = \frac{1}{3} (3 (2 u)) + \frac{1}{3} \cdot - 12$

Step 2.2.2

Cancel the common factor.

$- 2 + 3 u = \frac{1}{3} (3 (2 u)) + \frac{1}{3} \cdot - 12$

Step 2.2.3

Rewrite the expression.

$- 2 + 3 u = 2 u + \frac{1}{3} \cdot - 12$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $- 12$ .

$- 2 + 3 u = 2 u + \frac{1}{3} \cdot (3 (- 4))$

Step 2.3.2

Cancel the common factor.

$- 2 + 3 u = 2 u + \frac{1}{3} \cdot (3 \cdot - 4)$

Step 2.3.3

Rewrite the expression.

$- 2 + 3 u = 2 u - 4$

Step 3

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

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Step 3.1

Subtract $2 u$ from both sides of the equation.

$- 2 + 3 u - 2 u = - 4$

Step 3.2

Subtract $2 u$ from $3 u$ .

$- 2 + u = - 4$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$u = - 4 + 2$

Step 4.2

Add $- 4$ and $2$ .

$u = - 2$