Basic Math Examples

$\frac{3}{11} \cdot (w - 2) - \frac{60}{11} = - 6$

Step 1

Simplify $\frac{3}{11} \cdot (w - 2) - \frac{60}{11}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{3}{11} w + \frac{3}{11} \cdot - 2 - \frac{60}{11} = - 6$

Step 1.1.2

Combine $\frac{3}{11}$ and $w$ .

$\frac{3 w}{11} + \frac{3}{11} \cdot - 2 - \frac{60}{11} = - 6$

Step 1.1.3

Multiply $\frac{3}{11} \cdot - 2$ .

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Step 1.1.3.1

Combine $\frac{3}{11}$ and $- 2$ .

$\frac{3 w}{11} + \frac{3 \cdot - 2}{11} - \frac{60}{11} = - 6$

Step 1.1.3.2

Multiply $3$ by $- 2$ .

$\frac{3 w}{11} + \frac{- 6}{11} - \frac{60}{11} = - 6$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{3 w}{11} - \frac{6}{11} - \frac{60}{11} = - 6$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{3 w - 6 - 60}{11} = - 6$

Step 1.2.2

Subtract $60$ from $- 6$ .

$\frac{3 w - 66}{11} = - 6$

Step 1.2.3

Factor $3$ out of $3 w - 66$ .

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Step 1.2.3.1

Factor $3$ out of $3 w$ .

$\frac{3 (w) - 66}{11} = - 6$

Step 1.2.3.2

Factor $3$ out of $- 66$ .

$\frac{3 w + 3 \cdot - 22}{11} = - 6$

Step 1.2.3.3

Factor $3$ out of $3 w + 3 \cdot - 22$ .

$\frac{3 (w - 22)}{11} = - 6$

Step 2

Multiply both sides of the equation by $\frac{11}{3}$ .

$\frac{11}{3} \cdot \frac{3 (w - 22)}{11} = \frac{11}{3} \cdot - 6$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{11}{3} \cdot \frac{3 (w - 22)}{11}$ .

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Step 3.1.1.1

Cancel the common factor of $11$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{11}{3} \cdot \frac{3 (w - 22)}{11} = \frac{11}{3} \cdot - 6$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 (w - 22)) = \frac{11}{3} \cdot - 6$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{3} (3 (w - 22)) = \frac{11}{3} \cdot - 6$

Step 3.1.1.2.2

Rewrite the expression.

$w - 22 = \frac{11}{3} \cdot - 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{11}{3} \cdot - 6$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $- 6$ .

$w - 22 = \frac{11}{3} \cdot (3 (- 2))$

Step 3.2.1.1.2

Cancel the common factor.

$w - 22 = \frac{11}{3} \cdot (3 \cdot - 2)$

Step 3.2.1.1.3

Rewrite the expression.

$w - 22 = 11 \cdot - 2$

Step 3.2.1.2

Multiply $11$ by $- 2$ .

$w - 22 = - 22$

Step 4

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

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Step 4.1

Add $22$ to both sides of the equation.

$w = - 22 + 22$

Step 4.2

Add $- 22$ and $22$ .

$w = 0$