Let's solve the expression $\left(-9x - \frac{4}{5}\right) + \left(2x + \frac{2}{3}\right)$.

Step 1: Combine the like terms

Combine the $x$-terms:

$-9x + 2x = -7x$

Combine the constant terms:

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

Step 2: Find the common denominator of $\frac{4}{5}$ and $\frac{2}{3}$

The least common denominator of 5 and 3 is 15.

Rewrite the fractions: $-\frac{4}{5} = -\frac{12}{15}, \quad \frac{2}{3} = \frac{10}{15}$

Now add the fractions: $-\frac{12}{15} + \frac{10}{15} = -\frac{2}{15}$

Final Answer:

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

Would you like a more detailed explanation or help with related concepts?

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Related Questions:

1. How do you add and subtract algebraic expressions with rational coefficients?
2. What is the least common multiple, and how does it apply to fractions?
3. How do you simplify expressions involving negative signs?
4. What are other examples of algebraic operations involving fractions?
5. How can you convert improper fractions to decimals in algebra?

Tip: Always combine like terms (variables and constants) separately to keep algebraic expressions organized.