Problem 60 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(x+3\) when \(x=2\)

Step-by-Step Solution

Answer

The value of the expression \(x+3\) when \(x=2\) is 5.

Step 1: Identify the Expression and the Value of the Variable

The given equation is \(x+3\) and it is given that \(x=2\).

Step 2: Substitute the Value of the Variable into the Equation

Replace the \(x\) in the equation with \(2\) to get \(2+3\).

Step 3: Simplify the Expression

Perform the addition operation to get the final value of the expression, \(2+3=5\).

Key Concepts

Substitution in Expressions

Substitution is a technique used in algebra to replace variables in an expression with given values. This process allows us to evaluate expressions and find specific numerical results. To substitute appropriately, ensure you understand the equation and which variable values are provided.
In our exercise, we start with the expression \(x + 3\). We are told that \(x = 2\). The key to substitution is correctly identifying each occurrence of the variable that needs to be replaced.

• First, locate the variable \(x\) in the expression.
• Then, replace each \(x\) with the number \(2\).

After substitution, the expression \(x + 3\) transforms to \(2 + 3\). This approach simplifies the expression into one that can be further evaluated using arithmetic operations. Keeping track of your steps ensures no parts are missed or incorrectly replaced.

Simplifying Expressions

Simplifying expressions involves combining like terms and performing mathematical operations to reach a basic form. It's a vital skill in mathematics, allowing us to clarify and organize expressions for better understanding or further calculation.
Once we substitute the variable, as demonstrated previously, simplifying follows by executing simple arithmetic operations.

• Initially, with \(2 + 3\), there aren’t multiple like terms to combine, so we proceed directly to operations.
• Simplification often involves organizing expressions and ensuring each part is as simplified and functional as possible.

Careful adherence to mathematical rules during this process guarantees the correct and simplest result.

Basic Arithmetic Operations

Basic arithmetic operations such as addition, subtraction, multiplication, and division form the foundation of mathematics. These operations are the building blocks for evaluating and simplifying expressions.
In our example with \(2 + 3\), we perform an addition operation. Addition combines numbers or quantities to find their total:

• Identify that \(2 + 3\) is a straightforward addition, meaning we need to add 2 and 3 together.
• The sum of these numbers is \(5\).

Each arithmetic operation follows specific rules; understanding and applying them is crucial for accurately processing expressions. Mastery of these basics allows for tackling more complex mathematical challenges confidently.