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Chapter 1: Problem 3

Evaluate each expression for \(x=4\). $$12-x$$

Short Answer

Expert verified
The evaluated expression for \(x=4\) is 8.

Step by step solution

01

Understand the Expression

The expression given in the task is \(12 - x\). In this expression, \(x\) is a variable. In algebra, a variable is a letter that represents a number we don't know yet. In this particular task, the value of \(x\) is given, which is 4.
02

Substitute the Given Value

Replace the variable \(x\) in the expression with its given value. Hence, the new expression becomes \(12 - 4\).
03

Perform the Operation

The required operation in the expression is subtraction. Subtract 4 from 12, and the result is 8.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variables in Algebra
In algebra, variables are symbols or letters that represent unknown or changeable numbers. Commonly used letters are \(x\), \(y\), and \(z\), though any letter can work. The variable in an equation or expression signifies a number that may vary or is at times unknown. This concept allows us to create general mathematical models and solve problems flexibly.
For example, in the expression \(12 - x\), the \(x\) is a variable that can take on different values.
In different situations, before solving a problem, we often need to know the specific value of the variable.
  • Variables make mathematical expressions more dynamic
  • They can be adjusted to fit various real-world scenarios
  • Identifying variables is the first step in evaluating algebraic expressions
Substitution in Expressions
Substitution in algebra means replacing variables with their real values. This is a crucial step in evaluating expressions or equations. If the value of a variable is provided, as in our example where \(x = 4\), substitution allows us to find the numerical value of the expression.
Here's how it works:
1. Identify the variable in the expression. 2. Replace the variable with the given or known value.
In the expression \(12 - x\), substituting \(x\) with the value 4 gives us \(12 - 4\). Substitution simplifies the expression into a problem that involves basic arithmetic.
  • Substitution simplifies expressions for easier evaluation
  • It's useful in both simple and complex equations
  • It allows for the correct calculation of expressions
Basic Arithmetic Operations
Arithmetic operations are the foundation of mathematics, involving actions like addition, subtraction, multiplication, and division. These operations are crucial when solving algebraic expressions after substituting values.
In the expression \(12 - 4\), subtraction is the operation to be performed. Simple arithmetic tells us that subtracting 4 from 12 yields 8.
Key points to remember about basic arithmetic:
  • Subtraction reduces one value by another
  • Always perform operations in the proper order (following PEMDAS/BODMAS if needed)
  • Accurate arithmetic calculations lead to correct solutions
Subtraction, as demonstrated in this example, is straightforward and essential for obtaining precise results in variable-related expressions.

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