Problem 26 - Introductory and Intermediate Algebra for College Students 4th

Question

Write each English phrase as an algebraic expression. Let the variable \(x\) represent the number. six more than a number

Step-by-Step Solution

Answer

The algebraic expression is \(x + 6\).

Step 1: Identify Variable

The problem statement clearly indicates that \(x\) should be used to represent the number in question.

Step 2: Translate 'More Than'

The phrase 'more than' typically denotes an addition operation in algebra. The phrase 'six more than a number' can be translated as six plus that number, or in this case, six plus \(x\).

Step 3: Write the Algebraic Expression

The algebraic expression that represents 'six more than a number' is \(x + 6\).

Key Concepts

Understanding Variables

In algebra, a variable is like a placeholder or a symbol that represents an unknown number. In many problems, we use letters like \(x\), \(y\), or \(z\) to stand for these unknown values.
Since we don't know what the actual number is, we use a variable to represent this unknown quantity.
Imagine you're holding an empty box, and you don't know what's inside—it could be anything! The letter \(x\) works the same way; it's waiting to be filled with a number once we figure out what that number should be.
When you see \(x\) in a math problem, it just means "the number we're trying to find out."

• Variables can change: Just like the number inside the box can change, so can the value of a variable.
• Variables are useful: They help us write expressions and equations that can solve a wide range of problems!

Addition in Algebra

Addition in algebra allows us to combine numbers and terms to create algebraic expressions. When you see a phrase like 'six more than a number,' it's a hint that you need to add.
In words, the phrase 'more than' suggests an increase, which we show in math by using the plus sign \(+\).
In this scenario, 'six more than a number' implies we are taking our unknown number \(x\) and adding 6 to it.

Here's how addition in algebra works:

• Identify what you're adding: In our example, we're adding 6 to the variable \(x\).
• Write the addition: Simply place the number being added next to the variable with a plus sign, like \(x + 6\).
• Think of it like counting forward from the number: If \(x\) were 5, then adding 6 means counting forward 6 steps to get to 11.

By understanding and applying addition in algebra, you can easily construct expressions that represent various situations.

Translating Phrases to Expressions

Translating phrases into algebraic expressions is like turning words into math language.
This process involves finding operations such as addition, subtraction, multiplication, or division indicated by the words.
For 'six more than a number,' you recognize 'more than' as a signal for addition.

• Step 1: Spot the variable. Here, the variable is the unknown number \(x\).
• Step 2: Recognize the operation. The phrase mentions 'more than,' which means we add.
• Step 3: Form the expression. Add 6 to the variable, giving us \(x + 6\).

This translation is crucial because it helps solve real-world problems using algebraic methods. Each phrase connects directly to a math operation, making it easier to write and solve expressions accurately!
With practice, you'll gradually translate more complex phrases into algebraic expressions with ease.