Trigonometry Examples

$x + \frac{1}{7} = - \frac{2}{5}$

Step 1

Subtract $\frac{1}{7}$ from both sides of the equation.

$x = - \frac{2}{5} - \frac{1}{7}$

Step 2

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = - \frac{2}{5} \cdot \frac{7}{7} - \frac{1}{7}$

Step 3

To write $- \frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - \frac{2}{5} \cdot \frac{7}{7} - \frac{1}{7} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{5}$ by $\frac{7}{7}$ .

$x = - \frac{2 \cdot 7}{5 \cdot 7} - \frac{1}{7} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $7$ .

$x = - \frac{2 \cdot 7}{35} - \frac{1}{7} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{1}{7}$ by $\frac{5}{5}$ .

$x = - \frac{2 \cdot 7}{35} - \frac{5}{7 \cdot 5}$

Step 4.4

Multiply $7$ by $5$ .

$x = - \frac{2 \cdot 7}{35} - \frac{5}{35}$

Step 5

Combine the numerators over the common denominator.

$x = \frac{- 2 \cdot 7 - 5}{35}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 2$ by $7$ .

$x = \frac{- 14 - 5}{35}$

Step 6.2

Subtract $5$ from $- 14$ .

$x = \frac{- 19}{35}$

Step 7

Move the negative in front of the fraction.

$x = - \frac{19}{35}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{19}{35}$

Decimal Form:

$x = - 0.5\overline{428571}$