Problem 60 - Algebra 1: Concepts and Skills

Question

Which inequality is true? A) \(-9>-5\) B) \(9<5\) C) \(9<-5\) D) \(-9<5\)

Step-by-Step Solution

Answer

The correct answer is D. The inequality -9 < 5 is true.

Step 1: Analyse option A

The inequality -9 > -5 is not true because -5 is greater than -9 in the number line.

Step 2: Analyse option B

The inequality 9 < 5 is not true because 9 is greater than 5.

Step 3: Analyse option C

The inequality 9 < -5 is not true because 9 is greater than -5.

Step 4: Analyse option D

The inequality -9 < 5 is true because 5 is greater than -9 in the number line.

Key Concepts

Understanding the Number Line

A number line is a visual representation where numbers are ordered from left to right. The left side of the number line includes smaller numbers, while the right side holds larger numbers. This line is a simple yet powerful tool to understand the positions of numbers in relation to each other.
For instance, negative numbers are placed to the left of zero, as they are less than positive numbers. Zero acts as a pivot point between positive and negative values.
Using a number line allows us to visually see which numbers are larger or smaller, which can be a huge help when solving inequalities or ordering numbers.

Ordering Numbers

Ordering numbers is a fundamental concept that involves arranging numbers from smallest to largest or vice versa. This concept helps you to determine which of two numbers is greater or less, and it relies heavily on the idea of position on a number line.
Imagine you have a list of numbers: -9, -5, 0, 5, and 9. Using a number line, you would place -9 farthest to the left, then -5, then 0 in the center, followed by 5, and finally 9 at the far right. This arrangement makes it clear that -9 is the smallest and 9 is the largest number.

• This ordered sequence helps to quickly compare numbers.
• It's useful in everyday scenarios like sorting scores from a game or determining the winner based on higher numbers.

Integer Comparison

Integer comparison is the process of determining the relative size of integers. When comparing integers, it's vital to remember that negative numbers are always less than positive numbers.
For example, comparing integers like -9 and 5 involves recognizing that despite the digits, the negative symbol makes -9 less than 5. This is because -9 is to the left of 5 on the number line.

When comparing two negative numbers like -9 and -5, the number closer to zero (-5) is greater.

• Positive numbers are straightforward: the larger digit is greater.
• Integers are part of our daily lives, used in calculations, temperature readings, and financial statements.

Understanding integer comparisons helps solve inequalities efficiently and is a crucial part of mathematics.