Simplify (-9x-4/5)+(2x+2/3)

$(- 9 x - \frac{4}{5}) + (2 x + \frac{2}{3})$

Step 1

Remove parentheses.

$- 9 x - \frac{4}{5} + 2 x + \frac{2}{3}$

Step 2

Add $- 9 x$ and $2 x$ .

$- 7 x - \frac{4}{5} + \frac{2}{3}$

Step 3

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 7 x - \frac{4}{5} \cdot \frac{3}{3} + \frac{2}{3}$

Step 4

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 7 x - \frac{4}{5} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

$- 7 x - \frac{4 \cdot 3}{5 \cdot 3} + \frac{2}{3} \cdot \frac{5}{5}$

Multiply $5$ by $3$ .

$- 7 x - \frac{4 \cdot 3}{15} + \frac{2}{3} \cdot \frac{5}{5}$

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$- 7 x - \frac{4 \cdot 3}{15} + \frac{2 \cdot 5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$- 7 x - \frac{4 \cdot 3}{15} + \frac{2 \cdot 5}{15}$

Step 6

Combine the numerators over the common denominator.

$- 7 x + \frac{- 4 \cdot 3 + 2 \cdot 5}{15}$

Step 7

Simplify the numerator.

Multiply $- 4$ by $3$ .

$- 7 x + \frac{- 12 + 2 \cdot 5}{15}$

Multiply $2$ by $5$ .

$- 7 x + \frac{- 12 + 10}{15}$

Add $- 12$ and $10$ .

$- 7 x + \frac{- 2}{15}$

Step 8

Move the negative in front of the fraction.

$- 7 x - \frac{2}{15}$