Algebra Examples

$\frac{1}{3} w + \frac{5}{6} w - 2 = - w$

Step 1

Simplify $\frac{1}{3} w + \frac{5}{6} w - 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{3}$ and $w$ .

$\frac{w}{3} + \frac{5}{6} w - 2 = - w$

Step 1.1.2

Combine $\frac{5}{6}$ and $w$ .

$\frac{w}{3} + \frac{5 w}{6} - 2 = - w$

Step 1.2

To write $\frac{w}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{w}{3} \cdot \frac{2}{2} + \frac{5 w}{6} - 2 = - w$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{w}{3}$ by $\frac{2}{2}$ .

$\frac{w \cdot 2}{3 \cdot 2} + \frac{5 w}{6} - 2 = - w$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{w \cdot 2}{6} + \frac{5 w}{6} - 2 = - w$

Step 1.4

Combine the numerators over the common denominator.

$\frac{w \cdot 2 + 5 w}{6} - 2 = - w$

Step 1.5

Add $w \cdot 2$ and $5 w$ .

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Step 1.5.1

Reorder $w$ and $2$ .

$\frac{2 \cdot w + 5 w}{6} - 2 = - w$

Step 1.5.2

Add $2 \cdot w$ and $5 w$ .

$\frac{7 \cdot w}{6} - 2 = - w$

$\frac{7 w}{6} - 2 = - w$

Step 2

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

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Step 2.1

Add $w$ to both sides of the equation.

$\frac{7 w}{6} - 2 + w = 0$

Step 2.2

To write $w$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{7 w}{6} + w \cdot \frac{6}{6} - 2 = 0$

Step 2.3

Combine $w$ and $\frac{6}{6}$ .

$\frac{7 w}{6} + \frac{w \cdot 6}{6} - 2 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 w + w \cdot 6}{6} - 2 = 0$

Step 2.5

Add $7 w$ and $w \cdot 6$ .

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Step 2.5.1

Reorder $w$ and $6$ .

$\frac{7 w + 6 \cdot w}{6} - 2 = 0$

Step 2.5.2

Add $7 w$ and $6 \cdot w$ .

$\frac{13 w}{6} - 2 = 0$

Step 3

Add $2$ to both sides of the equation.

$\frac{13 w}{6} = 2$

Step 4

Multiply both sides of the equation by $\frac{6}{13}$ .

$\frac{6}{13} \cdot \frac{13 w}{6} = \frac{6}{13} \cdot 2$

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 $\frac{6}{13} \cdot \frac{13 w}{6}$ .

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Step 5.1.1.1

Cancel the common factor of $6$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{6}{13} \cdot \frac{13 w}{6} = \frac{6}{13} \cdot 2$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 w) = \frac{6}{13} \cdot 2$

Step 5.1.1.2

Cancel the common factor of $13$ .

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Step 5.1.1.2.1

Factor $13$ out of $13 w$ .

$\frac{1}{13} (13 (w)) = \frac{6}{13} \cdot 2$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{13} (13 w) = \frac{6}{13} \cdot 2$

Step 5.1.1.2.3

Rewrite the expression.

$w = \frac{6}{13} \cdot 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{6}{13} \cdot 2$ .

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Step 5.2.1.1

Combine $\frac{6}{13}$ and $2$ .

$w = \frac{6 \cdot 2}{13}$

Step 5.2.1.2

Multiply $6$ by $2$ .

$w = \frac{12}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$w = \frac{12}{13}$

Decimal Form:

$w = 0.\overline{923076}$