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Algebra is a branch of mathematics that helps us find unknown values using symbols. These symbols, often letters, are called variables. In our exercise, we have a variable, which is represented by the letter \( y \). This variable stands for Hector's current age. Variables are placeholders for numbers that we do not know yet. They help us work through the problem until we find the solution. In algebra, using variables allows us to write expressions. An expression is like a mathematical phrase that can include numbers, variables, and operations, such as addition or subtraction.When dealing with variables:

• Remember it's just a symbol for a number.
• Keep track of what each variable represents.
• Use it to form expressions that model real-life situations, like age.

Understanding how variables work is crucial to solving many algebraic problems.

Age-related word problems are common in basic algebra and usually involve finding someone's age at different times or comparing ages. These problems often use variables to represent the unknown ages. In our exercise, the problem is to find out Hector's age 5 years ago. To solve these:

• Start by identifying what you need to find. Here, it's Hector's age 5 years ago.
• Define the current age with a variable (\( y \)), and note any changes in age such as years ago or years into the future.
• Convert the word problem into an algebraic expression. Here, "5 years ago" translates to subtracting 5 years from Hector's current age \( y \).

These problems help improve problem-solving skills and apply algebra in practical contexts, making them an essential part of learning algebra.

Subtraction is one of the basic operations in mathematics, often signified with the minus (-) symbol. Subtraction is used to determine the difference between two numbers or to reduce the value of one number by another. In our example, we need to subtract 5 from the variable \( y \) to find out how old Hector was 5 years ago.Steps to perform simple subtraction in algebra:

• Identify the numbers or variables involved. We have \( y \) and 5 here.
• Arrange them following the subtraction statement, i.e., "\( y - 5 \)."
• Calculate the result, if numerical values for the variables are available. If not, just leave it as \( y - 5 \) to represent the expression.

Subtraction plays a vital role in many age-related problems, helping in the adjustment of values to reflect changes over time.