Algebra Examples

$- \frac{1}{4} w - 3 = w + \frac{1}{3}$

Step 1

Combine $w$ and $\frac{1}{4}$ .

$- \frac{w}{4} - 3 = w + \frac{1}{3}$

Step 2

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

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Step 2.1

Subtract $w$ from both sides of the equation.

$- \frac{w}{4} - 3 - w = \frac{1}{3}$

Step 2.2

To write $- w$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{w}{4} - w \cdot \frac{4}{4} - 3 = \frac{1}{3}$

Step 2.3

Combine $- w$ and $\frac{4}{4}$ .

$- \frac{w}{4} + \frac{- w \cdot 4}{4} - 3 = \frac{1}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- w - w \cdot 4}{4} - 3 = \frac{1}{3}$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $w$ out of $- w - w \cdot 4$ .

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Step 2.5.1.1.1

Factor $w$ out of $- w$ .

$\frac{w \cdot - 1 - w \cdot 4}{4} - 3 = \frac{1}{3}$

Step 2.5.1.1.2

Factor $w$ out of $- w \cdot 4$ .

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

Step 2.5.1.1.3

Factor $w$ out of $w \cdot - 1 + w (- 1 \cdot 4)$ .

$\frac{w (- 1 - 1 \cdot 4)}{4} - 3 = \frac{1}{3}$

Step 2.5.1.2

Multiply $- 1$ by $4$ .

$\frac{w (- 1 - 4)}{4} - 3 = \frac{1}{3}$

Step 2.5.1.3

Subtract $4$ from $- 1$ .

$\frac{w \cdot - 5}{4} - 3 = \frac{1}{3}$

Step 2.5.2

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

$\frac{- 5 \cdot w}{4} - 3 = \frac{1}{3}$

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{5 w}{4} - 3 = \frac{1}{3}$

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

$- \frac{5 w}{4} = \frac{1}{3} + 3$

Step 3.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5 w}{4} = \frac{1}{3} + 3 \cdot \frac{3}{3}$

Step 3.3

Combine $3$ and $\frac{3}{3}$ .

$- \frac{5 w}{4} = \frac{1}{3} + \frac{3 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{5 w}{4} = \frac{1 + 3 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $3$ .

$- \frac{5 w}{4} = \frac{1 + 9}{3}$

Step 3.5.2

Add $1$ and $9$ .

$- \frac{5 w}{4} = \frac{10}{3}$

Step 4

Multiply both sides of the equation by $- \frac{4}{5}$ .

$- \frac{4}{5} (- \frac{5 w}{4}) = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{4}{5} (- \frac{5 w}{4})$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{- 4}{5} (- \frac{5 w}{4}) = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.1.2

Move the leading negative in $- \frac{5 w}{4}$ into the numerator.

$\frac{- 4}{5} \cdot \frac{- 5 w}{4} = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{5} \cdot \frac{- 5 w}{4} = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{5} \cdot \frac{- 5 w}{4} = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 w) = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $- 5 w$ .

$\frac{- 1}{5} (5 (- w)) = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- w)) = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.2.3

Rewrite the expression.

$- - w = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 w = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.1.1.3.2

Multiply $w$ by $1$ .

$w = - \frac{4}{5} \cdot \frac{10}{3}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{4}{5} \cdot \frac{10}{3}$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$w = \frac{- 4}{5} \cdot \frac{10}{3}$

Step 5.2.1.1.2

Factor $5$ out of $10$ .

$w = \frac{- 4}{5} \cdot \frac{5 (2)}{3}$

Step 5.2.1.1.3

Cancel the common factor.

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

Step 5.2.1.1.4

Rewrite the expression.

$w = - 4 (\frac{2}{3})$

Step 5.2.1.2

Combine $- 4$ and $\frac{2}{3}$ .

$w = \frac{- 4 \cdot 2}{3}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $- 4$ by $2$ .

$w = \frac{- 8}{3}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$w = - \frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{8}{3}$

Decimal Form:

$w = - 2.\overline{6}$

Mixed Number Form:

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