Problem 59 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. $$ x - 5 \text { when } x=13 $$

Step-by-Step Solution

Answer

The evaluated expression when x equals 13 is 8.

Step 1: Substitution

Replace the variable \(x\) in the expression \(x - 5\) with 13. So the expression now becomes \(13 - 5\).

Step 2: Calculation

Perform the subtraction operation in the expression obtained from the substitution i.e. \(13 - 5 = 8\).

Key Concepts

Evaluating Expressions

Evaluating expressions is a fundamental skill in basic algebra that involves replacing variables with given numbers and then simplifying the expression. In this exercise, we evaluated the expression \( x - 5 \) when \( x = 13 \). What this means is that anytime you see the variable \( x \), you replace it with 13.
After substitution, the expression becomes \( 13 - 5 \). Then, you simply carry out the calculation, subtracting 5 from 13. In the end, you find that the expression equals 8. Evaluating expressions often requires repetition to become comfortable, so practice with similar problems is beneficial.

Basic Algebra

Basic algebra is the branch of mathematics dealing with expressions and operations involving variables. A variable is a symbol, often a letter, used to represent a number in an expression or equation.
In our exercise, the variable \( x \) stands for a specific number, 13. Basic algebra teaches you to work with these variables, replace them with numbers, and solve or simplify expressions.

• Substitution is a core technique in basic algebra.
• It involves "substituting" the variable with the given number.
• Understanding substitution helps in solving algebraic equations and expressions.

Knowing basic algebra opens up the door to more advanced mathematical concepts, so mastering these techniques early on is crucial.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations like addition and subtraction. They form the language of algebra and are used to describe mathematical relationships and solve problems.
For example, in the expression \( x - 5 \), \( x \) is the variable, and \(-5\) is a constant (a fixed number). Algebraic expressions can be simple, like this one, or more complex with multiple variables and operations. When working with algebraic expressions:

• Identify the variables and constants first.
• Recognize the operations involved—addition, subtraction, multiplication, or division.
• Substitute numbers into the variables to evaluate or simplify the expression.

Learning to manipulate algebraic expressions is key to solving equations, and it's important to familiarize yourself with these components as they form the basics of algebra. Understanding these elements makes tackling more complex algebraic equations more manageable.