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Variables are symbols used to represent unknown values in mathematical expressions or equations. In many cases, letters such as x, y, or z are chosen as variables. They act as placeholders for numbers that can change or that we need to find. For example, if a problem asks us to find a number that meets certain conditions, we can use x to represent this unknown number.
In the given exercise, the problem specifically instructs us to use x as the variable. This means every reference to 'a number' in the exercise can be replaced by x. Identifying the proper variable at the beginning simplifies the process of translating verbal phrases into mathematical expressions.

To recap, identifying variables is the first step in solving most algebraic problems. It allows you to transition from words to mathematical symbols, making it easier to apply operations like addition, subtraction, multiplication, and division.

In algebra, multiplication often involves combining numbers with variables. When the problem asks you to 'triple a number', it's instructing you to multiply that number by 3. Once a variable is identified, its multiplication by a constant—like 3—creates a term.
For example:

• Triple a number: 3 times the variable x is written as 3x.
• Double a number: 2 times the variable x is written as 2x.
• Quadruple a number: 4 times the variable x is written as 4x.

The process is intuitive once you grasp that the variable represents a number, and you simply multiply that variable by the given constant.

In the particular exercise mentioned above, tripling the variable x results in 3x. Completing this step converts part of the word problem into a mathematical term, making it easier to proceed with additional operations.

Subtraction in algebra helps us reduce or 'decrease' the value of an expression. Words like 'reduced by', 'minus', or 'decreased by' indicate subtraction. It is essential to perform this operation on the entire expression or term mentioned before the subtraction phrase.
Consider the exercise's phrase 'decreased by 14'. This phrase tells us to subtract 14 from the previously established term.

• First, we identified the variable x.
• Next, we tripled that variable to get 3x.
• Now, we subtract 14 from 3x, resulting in 3x - 14.

The order of operations is crucial here. We first perform multiplication (tripling the variable) and then subtraction (decreasing by 14).

Combining these steps correctly yields the final mathematical expression: 3x - 14. This expression translates the entire verbal phrase, maintaining all the operations in their required order.