Integer inequalities with absolute values

Learning Objectives Define absolute value as the distance from zero on a number line. Translate verbal descriptions into absolute value inequalities. Solve integer inequalities of the form |x| < c and |x| ≤ c. Solve integer inequalities of the form |x| > c and |x| ≥ c. Represent the integer solution set of an absolute value inequality on a number line. Interpret the solution of an absolute value inequality in a real-world context. A professional baker needs a cake to be baked at 180°C, but the oven temperature can vary by up to 3°C. How can we describe all the acceptable integer temperatures? 🤔 This lesson will teach you how to use absolute values to solve inequalities. You'll learn how absolute value represents a distance, which is key to understanding problems...

TermDefinitionExample IntegerA whole number that can be positive, negative, or zero. It does not have a fractional or decimal part.... -3, -2, -1, 0, 1, 2, 3 ... Absolute ValueThe distance of a number from zero on a number line. The absolute value is always a non-negative number.The absolute value of -5, written as |-5|, is 5 because -5 is 5 units away from 0. InequalityA mathematical statement that compares two values using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).x + 2 > 7 Solution SetThe set of all the integers that make an inequality true.For x > 3, the integer solution set is {4, 5, 6, ...}. Compound InequalityTwo inequalities joined together by the word 'and' or 'or'.'x > -2 and x...

The 'Less Than' Rule (AND Case) If |x| < c, then -c < x < c. The same rule applies for ≤. Use this rule when the absolute value is less than a positive number. It creates a single range of values, which is an 'and' compound inequality. Think 'less th-AND'. The 'Greater Than' Rule (OR Case) If |x| > c, then x > c OR x < -c. The same rule applies for ≥. Use this rule when the absolute value is greater than a positive number. It creates two separate ranges of values, which is an 'or' compound inequality. Think 'great-OR'.