Solve for s s+5/7=-1/2

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

Step 1

Subtract $\frac{5}{7}$ from both sides of the equation.

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

Step 2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$s = - \frac{7}{2 \cdot 7} - \frac{5}{7} \cdot \frac{2}{2}$

Multiply $2$ by $7$ .

$s = - \frac{7}{14} - \frac{5}{7} \cdot \frac{2}{2}$

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

$s = - \frac{7}{14} - \frac{5 \cdot 2}{7 \cdot 2}$

Multiply $7$ by $2$ .

$s = - \frac{7}{14} - \frac{5 \cdot 2}{14}$

Step 5

Combine the numerators over the common denominator.

$s = \frac{- 7 - 5 \cdot 2}{14}$

Step 6

Simplify the numerator.

Multiply $- 5$ by $2$ .

$s = \frac{- 7 - 10}{14}$

Subtract $10$ from $- 7$ .

$s = \frac{- 17}{14}$

Step 7

Move the negative in front of the fraction.

$s = - \frac{17}{14}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{17}{14}$

Decimal Form:

$s = - 1.21428571 \dots$

Mixed Number Form:

$s = - 1 \frac{3}{14}$