 # I can solve and graph inequalities containing the words and and or. 3.6 Compound Inequalities.

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I can solve and graph inequalities containing the words and and or. 3.6 Compound Inequalities

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 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: 3t + 2 < -7 or -4t + 5 < 1 3t < -9 or -4t < -4 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

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