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Combining like terms is a fundamental concept in algebra. Like terms are terms that contain the same variable raised to the same power. For instance, in the expression (5 + 9x) + (-4 - 8x), the terms 9x and -8x are like terms because they both have the variable x.
On the other hand, 5 and -4 are like terms because they are both constant terms.
When you combine like terms, you simply add or subtract their coefficients. For example, combining 9x and -8x would give you: 9x - 8x = x
This process helps to simplify the expression and makes it easier to work with in further calculations.
Combining like terms is essential for solving equations and simplifying expressions, making it a crucial skill in algebra.

Algebraic operations involve performing arithmetic on algebraic expressions. These operations include addition, subtraction, multiplication, and division.
In the given exercise, we primarily focus on addition and subtraction. For instance, in the expression (5 + 9x) + (-4 - 8x):

• First, you add the constants 5 and -4: 5 - 4 = 1.
• Next, you subtract the coefficients of the variable terms: 9x - 8x = x.

By doing these algebraic operations, you simplify the expression to its most basic form.Understanding algebraic operations helps to solve complex problems by breaking them down into simpler steps. It enables you to manipulate and transform expressions systematically.

The distributive property is another core concept in algebra. It states that a(b + c) is equal to ab + ac. Essentially, you distribute the multiplication over the addition or subtraction inside the parentheses.
In some cases, you will need the distributive property to simplify expressions before combining like terms. For example:

• If you have 2(3x + 4), you distribute 2 to both terms inside the parentheses: 2 * 3x + 2 * 4, which simplifies to 6x + 8.

While the given exercise (5 + 9x) + (-4 - 8x) did not specifically require the distributive property, understanding this concept is crucial for more complex problems.
The distributive property allows for greater flexibility and efficiency when simplifying expressions and solving equations.