Inequalities: Positive and Negative Numbers

Inequalities: Positive and Negative Numbers

Understanding the relationship between positive and negative numbers in inequalities

Introduction to Inequalities

• Inequalities compare two values and show their relationship.
• Positive numbers are greater than zero.
• Negative numbers are less than zero.
• Greater than symbol: >
• Less than symbol: <
• Greater than or equal to symbol: ≥
• Less than or equal to symbol: ≤

Multiple Choice

What symbols are used to compare two values in inequalities?

• >

• <

• ≥

• ≤

Inequality Symbols

Trivia: In inequalities, the symbol > is used to represent 'greater than', while the symbol < represents 'less than'. The symbols ≥ and ≤ are used for 'greater than or equal to' and 'less than or equal to', respectively. These symbols are commonly used in mathematics and logic to compare values and establish relationships between them.

Comparing Positive and Negative Numbers

• Positive numbers are greater than zero.
• Negative numbers are less than zero.
• When comparing positive and negative numbers, positive numbers are always greater than negative numbers.
• Zero is neither positive nor negative.

Multiple Choice

Which of the following statements is true about positive and negative numbers?

• Positive numbers are always greater than negative numbers.

• Negative numbers are always greater than positive numbers.

• Zero is considered a positive number.

• Zero is considered a negative number.

Positive vs Negative

Trivia: Positive numbers are always greater than negative numbers. This is because positive numbers are located to the right of zero on the number line, while negative numbers are located to the left. Zero is considered neither positive nor negative.

• Positive numbers are denoted with a '+' sign.
• Negative numbers are denoted with a '-' sign.
• Zero is the only number that is neither positive nor negative.

Using Number Lines for Comparison

Number lines are a helpful tool for comparing positive and negative numbers. To compare two numbers, plot them on a number line and observe their relative positions. Numbers to the right are greater, while numbers to the left are smaller. Use arrows to indicate the direction of comparison. Remember to consider the sign of the numbers when comparing.

Multiple Choice

What is the purpose of using number lines to compare positive and negative numbers?

• To determine the absolute value of a number

• To identify the smallest number

• To visualize the relative positions of numbers

• To calculate the sum of two numbers

Number Line:

To visualize the relative positions of numbers. Number lines help us understand the relationship between positive and negative numbers. They provide a visual representation of how numbers are ordered and their distance from zero. By using number lines, we can easily compare and determine the relative positions of different numbers.

Solving Inequalities

1. Identify the inequality sign (<, >, ≤, ≥). 2. Treat the inequality sign as an equal sign and solve the equation. 3. If the inequality sign is < or >, the solution is the set of all real numbers. 4. If the inequality sign is ≤ or ≥, include the endpoint in the solution set.

Multiple Choice

What is the solution set when the inequality sign is ≤ or ≥?

• The set of all real numbers

• The set of positive numbers

• The set of negative numbers

• The set of integers

Solution Set:

The solution set for inequalities with ≤ or ≥ is the set of all real numbers. This means that any real number can be a solution to the inequality. It includes positive numbers, negative numbers, and zero. The solution set is infinite and continuous. It represents a wide range of possible values.