Basic Math Examples

$\frac{3}{7} \cdot (w - 1) + \frac{1}{2} \cdot (w - 2) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1

Simplify $\frac{3}{7} \cdot (w - 1) + \frac{1}{2} \cdot (w - 2) + \frac{3}{2} \cdot (w - 6)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{3}{7} w + \frac{3}{7} \cdot - 1 + \frac{1}{2} \cdot (w - 2) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.2

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

$\frac{3 w}{7} + \frac{3}{7} \cdot - 1 + \frac{1}{2} \cdot (w - 2) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.3

Multiply $\frac{3}{7} \cdot - 1$ .

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Step 1.1.3.1

Combine $\frac{3}{7}$ and $- 1$ .

$\frac{3 w}{7} + \frac{3 \cdot - 1}{7} + \frac{1}{2} \cdot (w - 2) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.3.2

Multiply $3$ by $- 1$ .

$\frac{3 w}{7} + \frac{- 3}{7} + \frac{1}{2} \cdot (w - 2) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{3 w}{7} - \frac{3}{7} + \frac{1}{2} \cdot (w - 2) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.5

Apply the distributive property.

$\frac{3 w}{7} - \frac{3}{7} + \frac{1}{2} w + \frac{1}{2} \cdot - 2 + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.6

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

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} + \frac{1}{2} \cdot - 2 + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.7

Cancel the common factor of $2$ .

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Step 1.1.7.1

Factor $2$ out of $- 2$ .

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} + \frac{1}{2} \cdot (2 (- 1)) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.7.2

Cancel the common factor.

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} + \frac{1}{2} \cdot (2 \cdot - 1) + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.7.3

Rewrite the expression.

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} - 1 + \frac{3}{2} \cdot (w - 6) = 58$

Step 1.1.8

Apply the distributive property.

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} - 1 + \frac{3}{2} w + \frac{3}{2} \cdot - 6 = 58$

Step 1.1.9

Combine $\frac{3}{2}$ and $w$ .

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} - 1 + \frac{3 w}{2} + \frac{3}{2} \cdot - 6 = 58$

Step 1.1.10

Cancel the common factor of $2$ .

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Step 1.1.10.1

Factor $2$ out of $- 6$ .

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} - 1 + \frac{3 w}{2} + \frac{3}{2} \cdot (2 (- 3)) = 58$

Step 1.1.10.2

Cancel the common factor.

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} - 1 + \frac{3 w}{2} + \frac{3}{2} \cdot (2 \cdot - 3) = 58$

Step 1.1.10.3

Rewrite the expression.

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} - 1 + \frac{3 w}{2} + 3 \cdot - 3 = 58$

Step 1.1.11

Multiply $3$ by $- 3$ .

$\frac{3 w}{7} - \frac{3}{7} + \frac{w}{2} - 1 + \frac{3 w}{2} - 9 = 58$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$- 1 - 9 + \frac{3 w}{7} + \frac{- 3}{7} + \frac{w + 3 w}{2} = 58$

Step 1.2.2

Add $w$ and $3 w$ .

$- 1 - 9 + \frac{3 w}{7} + \frac{- 3}{7} + \frac{4 w}{2} = 58$

Step 1.3

Simplify each term.

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Step 1.3.1

Move the negative in front of the fraction.

$- 1 - 9 + \frac{3 w}{7} - \frac{3}{7} + \frac{4 w}{2} = 58$

Step 1.3.2

Cancel the common factor of $4$ and $2$ .

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Step 1.3.2.1

Factor $2$ out of $4 w$ .

$- 1 - 9 + \frac{3 w}{7} - \frac{3}{7} + \frac{2 (2 w)}{2} = 58$

Step 1.3.2.2

Cancel the common factors.

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Step 1.3.2.2.1

Factor $2$ out of $2$ .

$- 1 - 9 + \frac{3 w}{7} - \frac{3}{7} + \frac{2 (2 w)}{2 (1)} = 58$

Step 1.3.2.2.2

Cancel the common factor.

$- 1 - 9 + \frac{3 w}{7} - \frac{3}{7} + \frac{2 (2 w)}{2 \cdot 1} = 58$

Step 1.3.2.2.3

Rewrite the expression.

$- 1 - 9 + \frac{3 w}{7} - \frac{3}{7} + \frac{2 w}{1} = 58$

Step 1.3.2.2.4

Divide $2 w$ by $1$ .

$- 1 - 9 + \frac{3 w}{7} - \frac{3}{7} + 2 w = 58$

Step 1.4

Subtract $9$ from $- 1$ .

$- 10 + \frac{3 w}{7} - \frac{3}{7} + 2 w = 58$

Step 1.5

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 w}{7} - 10 \cdot \frac{7}{7} - \frac{3}{7} + 2 w = 58$

Step 1.6

Combine $- 10$ and $\frac{7}{7}$ .

$\frac{3 w}{7} + \frac{- 10 \cdot 7}{7} - \frac{3}{7} + 2 w = 58$

Step 1.7

Combine the numerators over the common denominator.

$\frac{3 w}{7} + \frac{- 10 \cdot 7 - 3}{7} + 2 w = 58$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Multiply $- 10$ by $7$ .

$\frac{3 w}{7} + \frac{- 70 - 3}{7} + 2 w = 58$

Step 1.8.2

Subtract $3$ from $- 70$ .

$\frac{3 w}{7} + \frac{- 73}{7} + 2 w = 58$

Step 1.9

Move the negative in front of the fraction.

$\frac{3 w}{7} - \frac{73}{7} + 2 w = 58$

Step 1.10

To write $2 w$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 w}{7} + 2 w \cdot \frac{7}{7} - \frac{73}{7} = 58$

Step 1.11

Combine $2 w$ and $\frac{7}{7}$ .

$\frac{3 w}{7} + \frac{2 w \cdot 7}{7} - \frac{73}{7} = 58$

Step 1.12

Combine the numerators over the common denominator.

$\frac{3 w + 2 w \cdot 7}{7} - \frac{73}{7} = 58$

Step 1.13

Combine the numerators over the common denominator.

$\frac{3 w + 2 w \cdot 7 - 73}{7} = 58$

Step 1.14

Multiply $7$ by $2$ .

$\frac{3 w + 14 w - 73}{7} = 58$

Step 1.15

Add $3 w$ and $14 w$ .

$\frac{17 w - 73}{7} = 58$

Step 2

Multiply both sides by $7$ .

$\frac{17 w - 73}{7} \cdot 7 = 58 \cdot 7$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $7$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{17 w - 73}{7} \cdot 7 = 58 \cdot 7$

Step 3.1.1.2

Rewrite the expression.

$17 w - 73 = 58 \cdot 7$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $58$ by $7$ .

$17 w - 73 = 406$

Step 4

Solve for $w$ .

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Step 4.1

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

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Step 4.1.1

Add $73$ to both sides of the equation.

$17 w = 406 + 73$

Step 4.1.2

Add $406$ and $73$ .

$17 w = 479$

Step 4.2

Divide each term in $17 w = 479$ by $17$ and simplify.

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Step 4.2.1

Divide each term in $17 w = 479$ by $17$ .

$\frac{17 w}{17} = \frac{479}{17}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $17$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{17 w}{17} = \frac{479}{17}$

Step 4.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{479}{17}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = \frac{479}{17}$

Decimal Form:

$w = 28.17647058 \dots$

Mixed Number Form:

$w = 28 \frac{3}{17}$