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Turning words into algebraic expressions is incredibly valuable in mathematics. It allows us to solve real-world problems using algebra. To translate verbal phrases into algebra, follow these steps:

First, identify your unknown variable, which is usually represented by letters like x or y.

If a phrase says 'a number', choose a variable to represent it. For example, let 'a number' be x.

Next, turn phrases like 'times', 'plus', 'less than' into mathematical operations. Example phrases and their translations include:

• 'Eight times a number' becomes 8x.
• 'Seventy-five less' translates to subtracting 75.

Combining these translations completes our algebraic expression. In our given exercise, 'Seventy-five less than eight times a number' translates to 8x - 75.

Basic algebra involves simple operations like addition, subtraction, multiplication, and division. It also means learning how to deal with variables, which are symbols that stand for unknown values.

In the exercise, our basic algebraic operations include:

Multiplication, as seen in 'eight times a number' (8x).
Subtraction, as indicated by 'seventy-five less' (subtract 75).

When you combine these operations correctly, you form an expression. The order of operations is important. Always perform multiplication or division before addition or subtraction unless parentheses say otherwise.

Algebra helps us solve equations, which are mathematical statements that show two expressions are equal. Mastering basic algebra is key to solving more complex math problems down the road.

An unknown variable is a symbol used to represent a number we do not know yet. It can be any letter, but commonly used ones are x, y, and z.

In our given problem, the phrase 'a number' is the unknown variable. We represent 'a number' by x.

Unknown variables are placeholders. In the exercise, we don't know the exact value of the number yet. But using x allows us to write and work with an expression like 8x - 75.

Solving any equation means finding the value of the variable. Here, if we had more information or an equation, we could solve for x. Understanding variables is fundamental to building algebraic expressions and solving equations.