Question

Evaluate the expression when \(x=2\). \(2 x\)

Short answer

The evaluated expression is 4.

Step-by-step solution

Identify the Given Values

The given values in the problem are \(x = 2\) and the expression which is \(2 x\).

Substitute the Value of x in the expression

Replace \(x\) in the equation \(2 x\) with the given value, which is 2. So, it becomes \(2 * 2\).

Solve the expression

Upon multiplication we get the result as 4.

Key concepts

Substituting Values

Grasping the concept of substituting values is like unlocking a door to the world of algebra. Imagine each variable like a box that can hold any number you choose. In our exercise, we have the box labeled with an 'x' and you're told to fill this box with the number 2.

Think of an algebraic expression as a recipe. If the recipe calls for 2 cups of sugar and you have the sugar, you simply add it in. Similarly, in algebra, when an expression like \(2 x\) asks for an 'x', you put in the value of 'x' that is provided. Here, since \(x = 2\), the expression \(2 x\) becomes \(2 \times 2\) when you replace 'x' with 2. This simple yet vital step transforms the algebraic expression into a numerical one, which you can then solve with basic arithmetic operations.

Expression Evaluation

Once you have substituted the variables with actual numbers, evaluating the expression is your next step. This process is like following through with a math recipe. Just as cooking requires you to mix ingredients in a specific order, evaluating expressions also has a sequence called the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In the given exercise, we don't have to worry about the order of operations since we only have to perform a single operation: multiplication. After substituting the value of 'x' with 2, we get \(2 \times 2\), which equals 4. Quick and simple: this is your answer, much like a two-step dish that leaves you with a tasty result, which in this case, is the solution to the expression.

Basic Algebra

Understanding basic algebra is akin to learning the alphabet of mathematics language. Let's break it down. Algebra involves using letters, called variables, to represent numbers. These can change depending on the situation, which is why they're called 'variables'. Equations and expressions are sentences in this mathematical language, conveying relationships between variables and constants.

In our example, \(2 x\) is an expression that uses the variable 'x' to stand in for a number. Variables make algebra powerful, as they allow us to describe patterns and relationships that hold true for many different numbers. For a beginner, mastering the concept of a variable and learning how to manipulate it through basic operations like addition, subtraction, multiplication, and division is paramount. Once you're comfortable performing these operations with variables, you've taken the first significant stride toward algebraic fluency.