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Chapter 1: Problem 4

Evaluate each expression for \(x=4\). $$16-x$$

Short Answer

Expert verified
The evaluated value of the expression \(16-x\) for \(x=4\) is 12.

Step by step solution

01

Identify the expression

The algebraic expression presented here is \(16-x\). This is the equation to be evaluated.
02

Substitute the value of x

The given value of x is 4. Now, substitute this value in the given expression, the equation becomes \(16-4\).
03

Solve the expression

Subtract 4 from 16. This gives the final evaluated value of the expression, which is 12.

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Key Concepts

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

Substitution
Substitution is a method used in algebra where you replace a variable in an algebraic expression with a given number. This process helps you evaluate expressions by calculating their numerical values once variables are replaced by numbers.
When you're given an expression to evaluate, like \(16 - x\), and a specific value for \(x\), the process is straightforward:
  • First, identify the variable present in the equation. In this case, it's \(x\).
  • Next, substitute \(x\) with the number provided. In our example, we substitute \(x\) with 4, changing the expression from \(16 - x\) to \(16 - 4\).
  • Finally, solve the simplified expression to find your answer.
Substitution is a fundamental skill in algebra that allows solving not just for single operations, but also for more complex equations involving multiple variables.
Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and mathematical operators, such as addition, subtraction, multiplication, and division. These expressions can represent real-life situations and often serve as the backbone of algebra problem-solving.
An example of an algebraic expression is \(16 - x\). Here, \(16\) is a constant (a fixed number), and \(x\) is a variable that can take on different values depending on the problem at hand.
  • Expressions can be as simple as a single variable or include multiple variables and complex operations.
  • Variables are used to represent unknown values, making algebraic expressions flexible tools for modeling different scenarios.
  • Understanding how to manipulate these expressions is key to solving algebra problems efficiently.
Grasping the concept of algebraic expressions is crucial for mastering algebra, as they form the basis for equations and other mathematical computations.
Basic Arithmetic Operations
Basic arithmetic operations form the foundation of mathematics and include addition, subtraction, multiplication, and division. These operations are essential for evaluating algebraic expressions after substitution.
In the problem \(16 - x\), once you substitute \(x\) with 4, the expression becomes \(16 - 4\). Now, you perform the following steps:
  • Subtraction is the specific operation required. Subtract 4 from 16.
  • This simple calculation results in 12, which is the evaluated value of the expression with the substituted variable.
Mastering these basic operations allows you to handle more complex arithmetic and algebraic problems with confidence. They are the building blocks for more advanced mathematical concepts, laying the groundwork for further studies in mathematics.

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