3 6 Compound Inequalities I can solve and

3. 6 Compound Inequalities I can solve and graph inequalities containing the words and or.

Compound Inequality �Consists of two distinct inequalities joined by the word and or the word or �You can find the solutions by identifying where the solutions overlap or by combining the solutions to form a larger solution set.

Using the word “And” �Contains the overlap of the graphs of two inequalities that form a compound inequality. �EX: x ≥ 3 and x ≤ 7 �Can also be written 3 ≤ x ≤ 7 �This is only for a compound inequality using the word “and”

Using the word “Or” �Contains each graph of the two inequalities that form the compound inequality. �Used when there is no overlap. �EX: x < -2 or x ≥ 1

Writing a Compound Inequality �All numbers that are greater than -2 and less than 6 �Key information �n > -2 and n < 6 �-2 < n < 6 �Graph

You try! �All real numbers that are less than 0 or greater than or equal to 5 �t < 0 or t ≥ 5

Solving �A solution to a compound inequality involving and is any number that makes both inequalities true. �EX: -3 ≤ m – 4 < -1 �Isolate the variable by adding 4 to each piece �-3 + 4 ≤ m – 4 + 4 < -1 + 4 � 1 ≤ m < 3

Solving �A solution to a compound inequality involving or is any number that makes either inequality true. �You must solve each inequality separately. �EX: 3 t + 2 < -7 or -4 t + 5 < 1 � 3 t < -9 or -4 t < -4 �t < -3 or t > 1

Writing and Solving �Multiply by 4 � 336 ≤ 86 + 85 + 80 + x ≤ 344 � 336 ≤ 251 + x ≤ 344 �Subtract 251 from each piece � 85 ≤ x ≤ 93

Interval Notation �Inequalities describe a portion of the number line or an interval. �Includes the use of 3 symbols

Practice �State each inequality in interval notation.

Assignment �ODDS ONLY �P. 204 #9 -29