Problem 27 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(12-x\) when \(x=3\)

Step-by-Step Solution

Answer

The evaluated expression is \(9\).

Step 1: Substitute the given value

Replace the variable \(x\) in the given expression \(12-x\) with the given value \(3\). So, the expression becomes \(12-3\).

Step 2: Perform the operation

Now perform the operation of subtraction. \(12 - 3 = 9\).

Key Concepts

Substitution Method

The substitution method is a key technique in algebra that helps to find the value of expressions when specific values for variables are known. It works by replacing variables in an expression with the values given. This method simplifies complex equations and expressions, making them easier to evaluate. For instance, if an expression given is \(12-x\), and you know \(x = 3\), you substitute 3 for \(x\) to find the result.

• Identify the variable in the expression.
• Find the given value for the variable.
• Replace the variable with the given numerical value to simplify the expression.

This straightforward method is applicable across various mathematical fields where evaluating expressions is necessary.

Variable Substitution

Variable substitution involves replacing a variable in an expression with a specific number or another expression. It's a foundational concept used not only in algebra but also in calculus and differential equations. A variable acts as a placeholder that represents a number we don't know yet or a number that can change. In our exercise, the expression is \(12-x\) and we substitute \(x\) with 3, changing the expression to \(12-3\).

• Recognize that each variable can be replaced by its corresponding value.
• This simplifies the expression into a basic arithmetic operation.

Variable substitution clarifies what an expression is supposed to represent, making it easier to solve or simplify.

Algebraic Operations

Algebraic operations refer to the basic mathematical operations performed within algebra, such as addition, subtraction, multiplication, and division. In evaluating expressions, these operations follow a specific order, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the provided exercise \(12-x\) becomes \(12-3\) once the variable is substituted, leading us to perform a simple subtraction.

• Ensure you are clear on what operation needs to be performed after substitution.
• Here, subtraction is performed because the expression stipulates a minus operation.
• Simple arithmetic operations like these help in checking the validity of complex algebraic expressions.

Always solve algebraic expressions step by step to arrive at a correct solution.