Trigonometry Examples

$\frac{4}{7} \cdot (w - 4) - \frac{19}{7} = - 5$

Step 1

Add $5$ to both sides of the equation.

$\frac{4}{7} \cdot (w - 4) - \frac{19}{7} + 5 = 0$

Step 2

Simplify $\frac{4}{7} \cdot (w - 4) - \frac{19}{7} + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{4}{7} w + \frac{4}{7} \cdot - 4 - \frac{19}{7} + 5 = 0$

Step 2.1.2

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

$\frac{4 w}{7} + \frac{4}{7} \cdot - 4 - \frac{19}{7} + 5 = 0$

Step 2.1.3

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

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Step 2.1.3.1

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

$\frac{4 w}{7} + \frac{4 \cdot - 4}{7} - \frac{19}{7} + 5 = 0$

Step 2.1.3.2

Multiply $4$ by $- 4$ .

$\frac{4 w}{7} + \frac{- 16}{7} - \frac{19}{7} + 5 = 0$

Step 2.1.4

Move the negative in front of the fraction.

$\frac{4 w}{7} - \frac{16}{7} - \frac{19}{7} + 5 = 0$

Step 2.2

Combine the numerators over the common denominator.

$5 + \frac{4 w - 16 - 19}{7} = 0$

Step 2.3

Subtract $19$ from $- 16$ .

$5 + \frac{4 w - 35}{7} = 0$

Step 2.4

To write $5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$5 \cdot \frac{7}{7} + \frac{4 w - 35}{7} = 0$

Step 2.5

Combine $5$ and $\frac{7}{7}$ .

$\frac{5 \cdot 7}{7} + \frac{4 w - 35}{7} = 0$

Step 2.6

Combine the numerators over the common denominator.

$\frac{5 \cdot 7 + 4 w - 35}{7} = 0$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $5$ by $7$ .

$\frac{35 + 4 w - 35}{7} = 0$

Step 2.7.2

Subtract $35$ from $35$ .

$\frac{4 w + 0}{7} = 0$

Step 2.7.3

Add $4 w$ and $0$ .

$\frac{4 w}{7} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.