Problem 3 - Beginning and Intermediate Algebra

Question

The sum of 15 and a number \(x\) is represented by A. \(15+x\) B. \(15-x\) C. \(x-15\) D. \(15 x\)

Step-by-Step Solution

Answer

A. 15 + x

Step 1 - Understand the Problem

The exercise asks to identify an algebraic expression that represents the sum of 15 and a number represented by the variable 'x'.

Step 2 - Summation in Algebra

In algebra, the term 'sum' refers to the result of addition. Therefore, the sum of two numbers means you need to add them together.

Step 3 - Identify the Correct Expression

To represent the sum of 15 and a number 'x', you need to use the addition operation. The correct expression that adds 15 to the variable 'x' is written as 15 + x.

Step 4 - Match with the Options Given

From the options provided, A. 15 + x B. 15 - x C. x - 15 D. 15x Only option A represents the sum of 15 and the number 'x'.

Key Concepts

Summation

Summation is a key concept in both arithmetic and algebra. It refers to the mathematical process of adding numbers together. When you see the word 'sum' in a problem, this always means you need to add something.
For example, if you have the numbers 3 and 5, the sum is obtained by:
In algebra, summation involves adding variables and constants. Variables are symbols that stand for unknown numbers. For instance, the sum of 15 and a variable 'x' is written as: 15 + x.
The summation operation follows the commutative property, which means that the order in which you add the numbers does not matter: x + y = y + x.

Addition in Algebra

Addition in algebra is similar to addition in basic arithmetic, but it can also involve variables. When adding variables, it's important to combine like terms. Like terms have the same variable raised to the same power.
For example, if you have 2x and 3x, you can add them together to get 5x. This is because both terms have the variable 'x'.
Let's look at a simple example involving a constant and a variable: If you want to find the sum of 7 and the variable 'y', you write it as: 7 + y.
It's important to know that we cannot add constants with variables directly unless they have the same variable parts.

Variable Representation

Variables are a cornerstone of algebra. They are symbols, often letters, that represent unknown values. Variables allow you to write general mathematical expressions and equations.
For instance, in the problem 'the sum of 15 and a number x', 'x' is the variable representing the unknown number. When the problem asks for the sum of 15 and 'x', it's simply instructing you to add 'x' to 15, giving you: 15 + x.
Variables can stand for any number, and you can manipulate them similarly to how you manipulate numbers. Understanding variable representation is crucial because it allows you to solve algebraic equations and understand abstract relationships.