Problem 50 - Algebra 1: Concepts and Skills

Question

Graph the numbers on a number line.Then write two inequalities that compare the numbers. $$-5,-2$$

Step-by-Step Solution

Answer

The two inequalities comparing the numbers -5 and -2 are \( -5 < -2 \) and \( -2 > -5 \)

Step 1: Graphing the Numbers

Given numbers are -5 and -2. Draw a number line and mark these numbers on it. The number -5 is to the left of -2 because on a number line, numbers increase from left to right.

Step 2: Write the Inequalities

An inequality compares two numerical values. Here, since -5 is less than -2, we can write the first inequality as \( -5 < -2 \). For the second inequality, we can reverse it and keep in mind that the signs change when we reverse an inequality, giving us \( -2 > -5 \).

Key Concepts

Understanding the Number Line

A number line is a visual tool that helps us comprehend the order and relationship of numbers. It is a horizontal line where numbers are placed at equal intervals. The numbers are arranged from smaller to larger, moving from left to right.

• The leftmost side features the smallest numbers, including negative numbers.
• As you move to the right, the numbers get larger.
• The number 0 is typically placed in the center.

For example, if we place -5 and -2 on a number line:
-5 is positioned to the left of -2 because -5 is less than -2. This visual placement helps in understanding that -5 is a smaller number compared to -2. The concept of placing numbers correctly is crucial when learning about inequalities, as it shows the relationship clearly and simply.

Graphing Numbers on a Number Line

Graphing numbers on a number line involves pinpointing their exact position according to their value. This practice helps in visualizing the size and order of the numbers, making complex concepts simpler.

• To begin, draw a straight horizontal line and mark a few points to serve as reference points, including 0, positive, and negative numbers.
• Next, position the given numbers on the line by ensuring they are placed according to their value.
• While graphing -5 and -2, you'll place -5 further left compared to -2 because it holds a lower value.

Seeing numbers on a number line helps reinforce the concept of numerical order, highlighting that negative numbers become smaller as they move further left.

Comparing Numbers and Inequalities

Comparing numbers often involves analyzing their relative size. An inequality is a mathematical expression used to show this comparison between two values.

• Inequalities use signs such as '<' (less than) and '>' (greater than).
• When comparing -5 and -2, you observe their positions on the number line.
• Since -5 is to the left of -2, it is smaller, so we write: \( -5 < -2 \).
• Conversely, reversing the inequality sign gives us the correct reading \( -2 > -5 \).

Understanding inequalities through the visual aid of a number line simplifies comprehension, making it easier to identify and compare values, even when dealing with negative numbers.