Algebra Examples

$- \frac{2}{5} w = 2 - \frac{1}{2} (3 - 5 w) - 2 w$

Step 1

Since $w$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 - \frac{1}{2} \cdot (3 - 5 w) - 2 w = - \frac{2}{5} w$

Step 2

Simplify $2 - \frac{1}{2} \cdot (3 - 5 w) - 2 w$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 - \frac{1}{2} \cdot 3 - \frac{1}{2} (- 5 w) - 2 w = - \frac{2}{5} w$

Step 2.1.2

Multiply $- \frac{1}{2} \cdot 3$ .

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Step 2.1.2.1

Multiply $3$ by $- 1$ .

$2 - 3 (\frac{1}{2}) - \frac{1}{2} (- 5 w) - 2 w = - \frac{2}{5} w$

Step 2.1.2.2

Combine $- 3$ and $\frac{1}{2}$ .

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

Step 2.1.3

Multiply $- \frac{1}{2} (- 5 w)$ .

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Step 2.1.3.1

Multiply $- 5$ by $- 1$ .

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

Step 2.1.3.2

Combine $5$ and $\frac{1}{2}$ .

$2 + \frac{- 3}{2} + \frac{5}{2} w - 2 w = - \frac{2}{5} w$

Step 2.1.3.3

Combine $\frac{5}{2}$ and $w$ .

$2 + \frac{- 3}{2} + \frac{5 w}{2} - 2 w = - \frac{2}{5} w$

Step 2.1.4

Move the negative in front of the fraction.

$2 - \frac{3}{2} + \frac{5 w}{2} - 2 w = - \frac{2}{5} w$

Step 2.2

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

$2 \cdot \frac{2}{2} - \frac{3}{2} + \frac{5 w}{2} - 2 w = - \frac{2}{5} w$

Step 2.3

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

$\frac{2 \cdot 2}{2} - \frac{3}{2} + \frac{5 w}{2} - 2 w = - \frac{2}{5} w$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - 3}{2} + \frac{5 w}{2} - 2 w = - \frac{2}{5} w$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

$\frac{4 - 3}{2} + \frac{5 w}{2} - 2 w = - \frac{2}{5} w$

Step 2.5.2

Subtract $3$ from $4$ .

$\frac{1}{2} + \frac{5 w}{2} - 2 w = - \frac{2}{5} w$

Step 2.6

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

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

Step 2.7

Combine $- 2 w$ and $\frac{2}{2}$ .

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

Step 2.8

Combine the numerators over the common denominator.

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

Step 2.9

Combine the numerators over the common denominator.

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

Step 2.10

Multiply $2$ by $- 2$ .

$\frac{1 + 5 w - 4 w}{2} = - \frac{2}{5} w$

Step 2.11

Subtract $4 w$ from $5 w$ .

$\frac{1 + w}{2} = - \frac{2}{5} w$

Step 3

Simplify $- \frac{2}{5} w$ .

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Step 3.1

Combine $w$ and $\frac{2}{5}$ .

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

Step 3.2

Move $2$ to the left of $w$ .

$\frac{1 + w}{2} = - \frac{2 w}{5}$

Step 4

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

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Step 4.1

Add $\frac{2 w}{5}$ to both sides of the equation.

$\frac{1 + w}{2} + \frac{2 w}{5} = 0$

Step 4.2

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

$\frac{1 + w}{2} \cdot \frac{5}{5} + \frac{2 w}{5} = 0$

Step 4.3

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

$\frac{1 + w}{2} \cdot \frac{5}{5} + \frac{2 w}{5} \cdot \frac{2}{2} = 0$

Step 4.4

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

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Step 4.4.1

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

$\frac{(1 + w) \cdot 5}{2 \cdot 5} + \frac{2 w}{5} \cdot \frac{2}{2} = 0$

Step 4.4.2

Multiply $2$ by $5$ .

$\frac{(1 + w) \cdot 5}{10} + \frac{2 w}{5} \cdot \frac{2}{2} = 0$

Step 4.4.3

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

$\frac{(1 + w) \cdot 5}{10} + \frac{2 w \cdot 2}{5 \cdot 2} = 0$

Step 4.4.4

Multiply $5$ by $2$ .

$\frac{(1 + w) \cdot 5}{10} + \frac{2 w \cdot 2}{10} = 0$

Step 4.5

Combine the numerators over the common denominator.

$\frac{(1 + w) \cdot 5 + 2 w \cdot 2}{10} = 0$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Apply the distributive property.

$\frac{1 \cdot 5 + w \cdot 5 + 2 w \cdot 2}{10} = 0$

Step 4.6.2

Multiply $5$ by $1$ .

$\frac{5 + w \cdot 5 + 2 w \cdot 2}{10} = 0$

Step 4.6.3

Move $5$ to the left of $w$ .

$\frac{5 + 5 \cdot w + 2 w \cdot 2}{10} = 0$

Step 4.6.4

Multiply $2$ by $2$ .

$\frac{5 + 5 w + 4 w}{10} = 0$

Step 4.6.5

Add $5 w$ and $4 w$ .

$\frac{5 + 9 w}{10} = 0$

Step 5

Set the numerator equal to zero.

$5 + 9 w = 0$

Step 6

Solve the equation for $w$ .

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Step 6.1

Subtract $5$ from both sides of the equation.

$9 w = - 5$

Step 6.2

Divide each term in $9 w = - 5$ by $9$ and simplify.

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Step 6.2.1

Divide each term in $9 w = - 5$ by $9$ .

$\frac{9 w}{9} = \frac{- 5}{9}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $9$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{9 w}{9} = \frac{- 5}{9}$

Step 6.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 5}{9}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Move the negative in front of the fraction.

$w = - \frac{5}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{5}{9}$

Decimal Form:

$w = - 0.\overline{5}$