Evaluate absolute value expressions

Learning Objectives Define absolute value as the distance of a number from zero on a number line. Identify and correctly use the absolute value symbol. Evaluate the absolute value of positive and negative integers. Evaluate absolute value expressions involving simple arithmetic operations inside the absolute value bars. Evaluate expressions that combine absolute values with other operations (addition, subtraction, multiplication) outside the absolute value bars. Apply the concept of absolute value to solve real-world problems involving distance or magnitude. Have you ever wondered how far you are from home, no matter which direction you walk? 🚶‍♀️🚶‍♂️ That's exactly what absolute value helps us figure out! In this lesson, you'll learn what absolute value means a...

TermDefinitionExample Absolute ValueThe absolute value of a number is its distance from zero on a number line. It is always a non-negative value (zero or positive).The absolute value of -5 is 5, because -5 is 5 units away from 0. The absolute value of 5 is also 5. Absolute Value SymbolThe symbol used to denote absolute value is two vertical bars surrounding a number or expression.$$|x|$$ means 'the absolute value of x'. So, $$|-7|$$ means 'the absolute value of -7'. IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero.$$... -3, -2, -1, 0, 1, 2, 3 ...$$ MagnitudeThe size or extent of something. In mathematics, it often refers to the absolute value of a number, ignoring its sign.The magnitude of -10 degrees Celsius is 10 degrees. The...

Definition of Absolute Value $$|x| = x \text{ if } x \ge 0$$ $$|x| = -x \text{ if } x < 0$$ This rule states that if the number inside the absolute value bars is positive or zero, its absolute value is the number itself. If the number inside is negative, its absolute value is the positive version of that number (which is achieved by multiplying the negative number by -1). Absolute Value of a Positive Number $$|a| = a \text{ if } a \text{ is positive}$$ The absolute value of any positive number is the number itself. For example, the distance of 7 from 0 is 7. Absolute Value of a Negative Number $$|-a| = a \text{ if } a \text{ is positive}$$ The absolute value of any negative number is its positive counterpart. For example, the distance of -7 from 0 is 7. Absol...