Is 3 a solution for the inequality x – 2 < 6? Lesson 2.1 Objective: To write and graph inequalities on a number line Vocabulary: Inequality is a statement that has an inequality symbol (>, <, >, <) Checking solutions Is 3 a solution for the inequality x – 2 < 6? Substitute 3 in for x 3 – 2 < 6 1 < 6 True

Decide if x – 6 > 8 when x = 13 Substitute 13 for x 13 – 6 > 8 7 > 8 False not a solution Decide if x + 2x < 30 when x = 9 Substitute 9 for both x’s 9 + 2(9) < 30 9 + 18 < 30 27 < 30 yes so 9 is a solution

Graphing Inequalities < > Means less than, under, fewer than. Uses an open circle when graphing Means greater than, more than, exceeds, higher. Uses an open circle when graphing Means less than or equal to, no more than, at most Uses a closed circle when graphing Means greater than or equal to, at least, no less than Uses a closed circle when graphing

VOCABULARY The graph of a linear inequality in one variable is the set of points on a number line that represent all solutions of the inequality. Verbal Phrase Inequality Graph All real numbers less than 3 All real numbers greater than –2 All real numbers less than or equal to 0 All real numbers greater than or equal to 2 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4

On your own Graph each inequality on a number line. 1) x < 10