Basic Math Examples

$7 w - \frac{7}{3} = - \frac{1}{3} w - \frac{7}{4}$

Step 1

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

$7 w - \frac{7}{3} = - \frac{w}{3} - \frac{7}{4}$

Step 2

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

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Step 2.1

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

$7 w - \frac{7}{3} + \frac{w}{3} = - \frac{7}{4}$

Step 2.2

To write $7 w$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$7 w \cdot \frac{3}{3} + \frac{w}{3} - \frac{7}{3} = - \frac{7}{4}$

Step 2.3

Combine $7 w$ and $\frac{3}{3}$ .

$\frac{7 w \cdot 3}{3} + \frac{w}{3} - \frac{7}{3} = - \frac{7}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 w \cdot 3 + w}{3} - \frac{7}{3} = - \frac{7}{4}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{7 w \cdot 3 + w - 7}{3} = - \frac{7}{4}$

Step 2.6

Multiply $3$ by $7$ .

$\frac{21 w + w - 7}{3} = - \frac{7}{4}$

Step 2.7

Add $21 w$ and $w$ .

$\frac{22 w - 7}{3} = - \frac{7}{4}$

Step 3

Multiply both sides by $3$ .

$\frac{22 w - 7}{3} \cdot 3 = - \frac{7}{4} \cdot 3$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{22 w - 7}{3} \cdot 3 = - \frac{7}{4} \cdot 3$

Step 4.1.1.2

Rewrite the expression.

$22 w - 7 = - \frac{7}{4} \cdot 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{7}{4} \cdot 3$ .

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Step 4.2.1.1

Multiply $- \frac{7}{4} \cdot 3$ .

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Step 4.2.1.1.1

Multiply $3$ by $- 1$ .

$22 w - 7 = - 3 (\frac{7}{4})$

Step 4.2.1.1.2

Combine $- 3$ and $\frac{7}{4}$ .

$22 w - 7 = \frac{- 3 \cdot 7}{4}$

Step 4.2.1.1.3

Multiply $- 3$ by $7$ .

$22 w - 7 = \frac{- 21}{4}$

Step 4.2.1.2

Move the negative in front of the fraction.

$22 w - 7 = - \frac{21}{4}$

Step 5

Solve for $w$ .

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Step 5.1

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

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Step 5.1.1

Add $7$ to both sides of the equation.

$22 w = - \frac{21}{4} + 7$

Step 5.1.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$22 w = - \frac{21}{4} + 7 \cdot \frac{4}{4}$

Step 5.1.3

Combine $7$ and $\frac{4}{4}$ .

$22 w = - \frac{21}{4} + \frac{7 \cdot 4}{4}$

Step 5.1.4

Combine the numerators over the common denominator.

$22 w = \frac{- 21 + 7 \cdot 4}{4}$

Step 5.1.5

Simplify the numerator.

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Step 5.1.5.1

Multiply $7$ by $4$ .

$22 w = \frac{- 21 + 28}{4}$

Step 5.1.5.2

Add $- 21$ and $28$ .

$22 w = \frac{7}{4}$

Step 5.2

Divide each term in $22 w = \frac{7}{4}$ by $22$ and simplify.

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Step 5.2.1

Divide each term in $22 w = \frac{7}{4}$ by $22$ .

$\frac{22 w}{22} = \frac{\frac{7}{4}}{22}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $22$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{22 w}{22} = \frac{\frac{7}{4}}{22}$

Step 5.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{\frac{7}{4}}{22}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$w = \frac{7}{4} \cdot \frac{1}{22}$

Step 5.2.3.2

Multiply $\frac{7}{4} \cdot \frac{1}{22}$ .

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Step 5.2.3.2.1

Multiply $\frac{7}{4}$ by $\frac{1}{22}$ .

$w = \frac{7}{4 \cdot 22}$

Step 5.2.3.2.2

Multiply $4$ by $22$ .

$w = \frac{7}{88}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$w = \frac{7}{88}$

Decimal Form:

$w = 0.079\overline{54}$