Graph compound inequalities

Learning Objectives Define a compound inequality and differentiate between 'and' (intersection) and 'or' (union) statements. Correctly use open and closed circles on a number line to represent inequality symbols. Graph compound inequalities involving 'and' on a number line. Graph compound inequalities involving 'or' on a number line. Solve multi-step compound inequalities before graphing their solution sets. Translate a graphed compound inequality from a number line into its algebraic form. Ever seen a sign that says 'You must be between 48" and 60" tall to ride this roller coaster'? 🎢 You've just encountered a real-world compound inequality! This tutorial will teach you how to represent two inequalities at t...

TermDefinitionExample Compound InequalityTwo or more inequalities joined together by the words 'and' or 'or'.`x > 5` and `x \le 10` is a compound inequality. Another example is `x < 0` or `x \ge 3`. Intersection ('and')The solution set for an 'and' inequality includes all numbers that make *both* inequalities true. The graph shows the overlapping shaded region.The inequality `-2 < x \le 4` means 'x is greater than -2' AND 'x is less than or equal to 4'. The number 3 is a solution because it satisfies both conditions. Union ('or')The solution set for an 'or' inequality includes all numbers that make *at least one* of the inequalities true. The graph shows all shaded regions combined.The inequality `x &...

Graphing 'And' Inequalities For `a < x \le b`, the graph is a single line segment between `a` and `b`. This represents an intersection. Place the appropriate circles at endpoints `a` and `b` and shade the region *between* them. This compact form is equivalent to `x > a` and `x \le b`. Graphing 'Or' Inequalities For `x < a` or `x > b` (where `a < b`), the graph consists of two rays pointing in opposite directions. This represents a union. Graph the first inequality and then graph the second inequality on the same number line. The final graph is the combination of both, typically pointing away from each other. The Sign-Flipping Rule If you multiply or divide both sides of an inequality by a negative number, you MUST flip the direction o...