Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $w$ and $\frac{3}{5}$ .

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

Step 1.2

Move $3$ to the left of $w$ .

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

Step 2

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

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Step 2.1

Add $\frac{3 w}{5}$ to both sides of the equation.

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

Step 2.2

To write $- 6 w$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Multiply $5$ by $- 6$ .

$\frac{- 30 w + 3 w + 1}{5} = - \frac{1}{3}$

Step 2.7

Add $- 30 w$ and $3 w$ .

$\frac{- 27 w + 1}{5} = - \frac{1}{3}$

Step 2.8

Factor $- 1$ out of $- 27 w$ .

$\frac{- (27 w) + 1}{5} = - \frac{1}{3}$

Step 2.9

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- (27 w) - 1 (- 1)}{5} = - \frac{1}{3}$

Step 2.10

Factor $- 1$ out of $- (27 w) - 1 (- 1)$ .

$\frac{- (27 w - 1)}{5} = - \frac{1}{3}$

Step 2.11

Rewrite $- (27 w - 1)$ as $- 1 (27 w - 1)$ .

$\frac{- 1 (27 w - 1)}{5} = - \frac{1}{3}$

Step 2.12

Move the negative in front of the fraction.

$- \frac{27 w - 1}{5} = - \frac{1}{3}$

Step 3

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{27 w - 1}{5}) = - 5 (- \frac{1}{3})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 5 (- \frac{27 w - 1}{5})$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{27 w - 1}{5}$ into the numerator.

$- 5 \frac{- (27 w - 1)}{5} = - 5 (- \frac{1}{3})$

Step 4.1.1.1.2

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- (27 w - 1)}{5} = - 5 (- \frac{1}{3})$

Step 4.1.1.1.3

Cancel the common factor.

$5 \cdot - 1 \frac{- (27 w - 1)}{5} = - 5 (- \frac{1}{3})$

Step 4.1.1.1.4

Rewrite the expression.

$- - (27 w - 1) = - 5 (- \frac{1}{3})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (27 w - 1) = - 5 (- \frac{1}{3})$

Step 4.1.1.2.2

Multiply $27 w - 1$ by $1$ .

$27 w - 1 = - 5 (- \frac{1}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 5 (- \frac{1}{3})$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 5$ .

$27 w - 1 = 5 (\frac{1}{3})$

Step 4.2.1.2

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

$27 w - 1 = \frac{5}{3}$

Step 5

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

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Step 5.1

Add $1$ to both sides of the equation.

$27 w = \frac{5}{3} + 1$

Step 5.2

Write $1$ as a fraction with a common denominator.

$27 w = \frac{5}{3} + \frac{3}{3}$

Step 5.3

Combine the numerators over the common denominator.

$27 w = \frac{5 + 3}{3}$

Step 5.4

Add $5$ and $3$ .

$27 w = \frac{8}{3}$

Step 6

Divide each term in $27 w = \frac{8}{3}$ by $27$ and simplify.

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Step 6.1

Divide each term in $27 w = \frac{8}{3}$ by $27$ .

$\frac{27 w}{27} = \frac{\frac{8}{3}}{27}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $27$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{27 w}{27} = \frac{\frac{8}{3}}{27}$

Step 6.2.1.2

Divide $w$ by $1$ .

$w = \frac{\frac{8}{3}}{27}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$w = \frac{8}{3} \cdot \frac{1}{27}$

Step 6.3.2

Multiply $\frac{8}{3} \cdot \frac{1}{27}$ .

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Step 6.3.2.1

Multiply $\frac{8}{3}$ by $\frac{1}{27}$ .

$w = \frac{8}{3 \cdot 27}$

Step 6.3.2.2

Multiply $3$ by $27$ .

$w = \frac{8}{81}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$w = \frac{8}{81}$

Decimal Form:

$w = 0.09876543 \dots$