Precalculus Examples

$4 (\frac{5}{18}) + 7 w - 7 (\frac{11}{72}) = 6$

Step 1

Simplify $4 (\frac{5}{18}) + 7 w - 7 (\frac{11}{72})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $2$ .

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Step 1.1.1.1

Factor $2$ out of $4$ .

$2 (2) \frac{5}{18} + 7 w - 7 (\frac{11}{72}) = 6$

Step 1.1.1.2

Factor $2$ out of $18$ .

$2 \cdot 2 \frac{5}{2 \cdot 9} + 7 w - 7 (\frac{11}{72}) = 6$

Step 1.1.1.3

Cancel the common factor.

$2 \cdot 2 \frac{5}{2 \cdot 9} + 7 w - 7 (\frac{11}{72}) = 6$

Step 1.1.1.4

Rewrite the expression.

$2 (\frac{5}{9}) + 7 w - 7 (\frac{11}{72}) = 6$

Step 1.1.2

Combine $2$ and $\frac{5}{9}$ .

$\frac{2 \cdot 5}{9} + 7 w - 7 (\frac{11}{72}) = 6$

Step 1.1.3

Multiply $2$ by $5$ .

$\frac{10}{9} + 7 w - 7 (\frac{11}{72}) = 6$

Step 1.1.4

Multiply $- 7 (\frac{11}{72})$ .

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Step 1.1.4.1

Combine $- 7$ and $\frac{11}{72}$ .

$\frac{10}{9} + 7 w + \frac{- 7 \cdot 11}{72} = 6$

Step 1.1.4.2

Multiply $- 7$ by $11$ .

$\frac{10}{9} + 7 w + \frac{- 77}{72} = 6$

Step 1.1.5

Move the negative in front of the fraction.

$\frac{10}{9} + 7 w - \frac{77}{72} = 6$

Step 1.2

To write $\frac{10}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$7 w + \frac{10}{9} \cdot \frac{8}{8} - \frac{77}{72} = 6$

Step 1.3

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{10}{9}$ by $\frac{8}{8}$ .

$7 w + \frac{10 \cdot 8}{9 \cdot 8} - \frac{77}{72} = 6$

Step 1.3.2

Multiply $9$ by $8$ .

$7 w + \frac{10 \cdot 8}{72} - \frac{77}{72} = 6$

Step 1.4

Combine the numerators over the common denominator.

$7 w + \frac{10 \cdot 8 - 77}{72} = 6$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $10$ by $8$ .

$7 w + \frac{80 - 77}{72} = 6$

Step 1.5.2

Subtract $77$ from $80$ .

$7 w + \frac{3}{72} = 6$

Step 1.6

Cancel the common factor of $3$ and $72$ .

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Step 1.6.1

Factor $3$ out of $3$ .

$7 w + \frac{3 (1)}{72} = 6$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $72$ .

$7 w + \frac{3 \cdot 1}{3 \cdot 24} = 6$

Step 1.6.2.2

Cancel the common factor.

$7 w + \frac{3 \cdot 1}{3 \cdot 24} = 6$

Step 1.6.2.3

Rewrite the expression.

$7 w + \frac{1}{24} = 6$

Step 2

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

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Step 2.1

Subtract $\frac{1}{24}$ from both sides of the equation.

$7 w = 6 - \frac{1}{24}$

Step 2.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$7 w = 6 \cdot \frac{24}{24} - \frac{1}{24}$

Step 2.3

Combine $6$ and $\frac{24}{24}$ .

$7 w = \frac{6 \cdot 24}{24} - \frac{1}{24}$

Step 2.4

Combine the numerators over the common denominator.

$7 w = \frac{6 \cdot 24 - 1}{24}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $6$ by $24$ .

$7 w = \frac{144 - 1}{24}$

Step 2.5.2

Subtract $1$ from $144$ .

$7 w = \frac{143}{24}$

Step 3

Divide each term in $7 w = \frac{143}{24}$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 w = \frac{143}{24}$ by $7$ .

$\frac{7 w}{7} = \frac{\frac{143}{24}}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 w}{7} = \frac{\frac{143}{24}}{7}$

Step 3.2.1.2

Divide $w$ by $1$ .

$w = \frac{\frac{143}{24}}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$w = \frac{143}{24} \cdot \frac{1}{7}$

Step 3.3.2

Multiply $\frac{143}{24} \cdot \frac{1}{7}$ .

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Step 3.3.2.1

Multiply $\frac{143}{24}$ by $\frac{1}{7}$ .

$w = \frac{143}{24 \cdot 7}$

Step 3.3.2.2

Multiply $24$ by $7$ .

$w = \frac{143}{168}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$w = \frac{143}{168}$

Decimal Form:

$w = 0.85119047 \dots$