 # Compound Inequalities

## Presentation on theme: "Compound Inequalities"— Presentation transcript:

Compound Inequalities
What you’ll learn To solve and graph inequalities containing the word and. To solve inequalities containing the word or Vocabulary Compound inequality: A compound inequalities consists of two distinct inequalities joined by the word and or the word or. Interval notation: includes the use of the three special symbols.

Writing a compound inequality
Example 1:What compound inequality represents the phrase? Graph the solutions. All real numbers that are greater than -2 and less than 6 n›-2 and n‹6 -2‹n and n‹6 -2‹n‹6 B. All real numbers that are less than 0 or greater than or equal to 5 t‹0 or t≥5

Your turn What compound inequality represents the phrase? Graph the solutions. All real numbers that are greater than or equal to -4 and less than 6 n≥-4 and n<6 -4≤n<6 B. All real numbers that are less than or equal to or greater than 6 =2.5 n≤2.5 or n>6

Solving a compound inequality involving and
or Note: a solution of a compound inequality involving and is any number that makes both inequalities true. You can solve this inequality both ways.

Solving a compound inequality involving or
Note: A solution of a compound inequality involving or is an number that makes either inequality true. You must solve them separately.

Your turn What are the solutions of? Graph the inequalities A. -5 < 3y-4 < 14 Answers: B.-2y+7 < 1 or 4y+3 ≤ -5 Answers: y>3 or y≤2

the compound inequality
Writing and Solving a Compound Inequality To earn a B in your algebra course, you must achieve an unrounded test average between 84 and 86, inclusive. You scored 86,85, and 80 on the first three test of the grading period. What possible scores can you earn on the fourth and final test a B in the course Need Possible scores you can earn on the last test to get a B in the course Plan Write an expression for you test average. Then write and solve the compound inequality Know Test average must be between 84 and 86, inclusive. The first 3 test scores Your score on the fourth test must be between 85 and 93, inclusive

Your turn To win the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive. Suppose you collected 82, 86,and 84 pop tabs during the first three weeks of the competition. What are the possible numbers of pop tabs you can collect during the fourth and final week in order to win the recycling contest? Answer: between 80 and 96 pop tabs inclusive

Using Interval Notation
1.What is the graph [-4,6)? How do you write [-4,6) as an inequality? The parenthesis indicates that 6 is not included. So use an open circle at 6. The bracket indicates that -4 is included. So use a closed circle at -4. -4 ≤ x < 6 2.What is the graph of x ≤ -1 or x>2? How do you write x≤-1 or x>2 in interval notation. The interval or

Classwork odd Homework even
Pgs exercises 9-41