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In algebra, an expression is a combination of numbers, variables, and operators (such as +, −, ×, ÷) arranged in a meaningful way. Expressions do not have an equality sign, unlike equations. Here, the given expression is \(3y\).

With expressions, you can perform various operations which can alter its form but not its value. You may see expressions like \(x + 5\), \(4z^2\), or \(a^3 - 2a\). Each of these is an expression that can be evaluated, combined, or simplified.

It's important to understand that expressions are foundational in algebra. They allow mathematicians to represent problems in a more flexible way. This helps in creating models that can describe the world around us. Expressions can include:

• Variables: like \(x, y, z\), which represent unknown values or quantities that can change.
• Constants: like numbers (2, 5, -3) which do not change.
• Operations: like addition, subtraction, multiplication, and division.

Understanding expressions is essential for solving algebraic problems.

Substitution is a fundamental technique in algebra. It involves replacing a variable with a given value or another expression. In this exercise, substitution is used to replace \(y\) in \(3y\) with the expression \(x-1\), forming \(3(x-1)\).

To perform substitution, follow these steps:

• Identify the variable to be substituted and find its equivalent expression or value.
• Replace each occurrence of that variable in the expression or equation.
• Ensure that you substitute correctly by checking that the new expression is accurate.

Substitution is particularly useful when trying to express a variable in terms of another variable. It's also a skill you'll frequently use in solving algebraic equations. Through practice, you can easily spot when and how to use substitution effectively.

It simplifies problems by making complex expressions more manageable or reducing the number of variables involved.

Simplification aims to make an expression easier to work with or understand. This often involves combining like terms or using properties such as the distributive property. In our problem, simplifying \(3(x-1)\) involves distributing the 3 across \(x-1\), resulting in \(3x-3\).

Here's how you can simplify expressions:

• Distribute any coefficients across terms inside parentheses. For example, \(a(b+c)\) becomes \(ab+ac\).
• Combine like terms, which are terms with the same variables raised to the same power, such as \(2x + 3x = 5x\).
• Eliminate any unnecessary parentheses if they do not alter the expression's meaning.

Simplification is a key step in manipulating algebraic expressions because it makes them easier to interpret or solve, especially when dealing with large or complex equations.

When you're simplifying, ensure you follow the rules of arithmetic and algebra thoroughly to avoid mistakes and achieve the correct form of the expression.