For Math 1009 class in ULM use only, these notes are not to be used without written permission of editors - Liu,Ji,Morris. 1.7 Linear Inequalities Objectives: Practice solving linear inequalities. Represent the solution sets of inequalities in interval notation and on a number line. Solve application questions using linear inequalities. Interval Notation: INEQUALITY NUMBER LINE GRAPH NOTATION INTERVAL NOTATION >7 4 <0 3 1<4 2> > 5 Important Note: when you MULTIPLY or DIVIDE both sides of an inequality by a NEGATIVE number, you must REVERSE the direction of the inequality symbol. Always graph on your scratch paper first, then write in interval notation. Interval Notation: 1) Order matters: place the smaller number on the Left and the bigger number on Right 2) For "", always use "(", "" always use ")". 3) With the equal sign use "[ ", "]", without he equal sign use "(",")". For Math 1009 class in ULM use only, these notes are not to be used without written permission of editors - Liu,Ji,Morris. Problem Type 1: Solve the inequality and express your answers your answer in interval notation. (1) 518<10.8+3 (2) 5<3216 (3) 42(5)<6 (4) 1.613.44.6(1) (5) 10 < +3 18 848 76 (6) 6+4.4 > 5+3.2 For Math 1009 class in ULM use only, these notes are not to be used without written permission of editors - Liu,Ji,Morris. Problem Type 2: Applications of Linear Inequality (1) In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Frank has scored 79, 75, and 88 on the first three. What range of scores on the fourth test will give Frank a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value. Express your answer in interval notation. (2) In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, David has scored 86, 78, and 88 on the first three. What range of scores on the fourth test will give David a B for the semester (an average between 80 and 89, inclusive)? Assume that all test scores have a non-negative value. Express your answer in interval notation. For Math 1009 class in ULM use only, these notes are not to be used without written permission of editors - Liu,Ji,Morris. (3) Maya owns an orange grove and needs to harvest at least 2724 oranges to cover the costs of running the grove. If each tree bears an average of 76 oranges and Maya wants to donate 240 oranges to charity, how many orange trees need to be in the grove? Express your answer in interval notation