Absolute value and opposite integers

Learning Objectives Define integers and locate them accurately on a number line. Explain the concept of absolute value as the distance of a number from zero. Calculate the absolute value of any given integer. Identify the opposite of any given integer. Compare and order integers using their absolute values. Solve mathematical expressions involving absolute value and opposite integers. Have you ever wondered how far you are from home, regardless of whether you're east or west? 📍 This lesson will help us measure 'distance' in math, no matter the direction! In this lesson, we'll explore absolute value and opposite integers, fundamental concepts for understanding numbers beyond just positive values. Mastering these ideas is crucial for working with linear f...

TermDefinitionExample IntegerIntegers are whole numbers (positive, negative, or zero) that can be written without a fractional or decimal component. Examples include -3, 0, 5.The set of integers includes ..., -3, -2, -1, 0, 1, 2, 3, ... Number LineA number line is a straight line on which every point corresponds to a real number, with zero usually at the center, positive numbers to the right, and negative numbers to the left.To locate -4 on a number line, you would move 4 units to the left of 0. Absolute ValueThe absolute value of an integer is its distance from zero on the number line. It is always a non-negative value.The absolute value of -7 is 7, written as |-7| = 7. The absolute value of 7 is also 7, written as |7| = 7. Opposite IntegersOpposite integers are two integers that are the...

Absolute Value Notation $$|x|$$ The absolute value of a number 'x' is denoted by two vertical bars surrounding the number. For example, $|-5|$ means 'the absolute value of negative five'. Definition of Absolute Value $$|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$$ If a number 'x' is positive or zero, its absolute value is 'x' itself. If 'x' is negative, its absolute value is the opposite of 'x' (which makes it positive). Finding the Opposite of an Integer $$ \text{Opposite of } x \text{ is } -x $$ To find the opposite of any integer, simply change its sign. If it's positive, make it negative. If it's negative, make it positive. The opposite of 0 is 0....