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Due: ___________________ Corrections Needed: Name: Math 95: Solving Linear Inequalities and Absolute Value Where to look in your ALEKS pie: In the “Real Numbers and Linear Equations” slice, look for anything with “inequality” in the title. For the graphing problems with two variables, look in “Graphs and Linear Functions” for “Graphing a linear inequality in the plane” (there are a few problem types). Interval notation is also dealt with in the “Graphs and Linear Functions” slice. Directions: Please show your work. For Exercises 1-3, solve the inequality and express your answer using interval notation. Then graph your solution set on a number line. Exercise 1: 3𝑥 + 1 ≤ 10 Exercise 2: 9 − 𝑥 < 16 Exercise 3: −1 ≤ 2𝑥 − 3 < 19 Exercise 4: Graph the solution set on a number line: 𝑥 ≤ −2 or 𝑥 > 3 For Exercises 5 and 6, solve the inequality and express your answer using interval notation. Then graph your solution set on a number line. Exercise 5: |𝑥 − 4| ≤ 3 Exercise 6: |2𝑥 − 3| > 13 Exercise 7: Explain why every real number x is a solution of the inequality |8𝑥 − 13| > −15. _____________________________________________________________________________________ _____________________________________________________________________________________ Exercise 8: Graph the solution set on a number line: 4|𝑥 − 2| + 6 < 18 Exercise 9: A student knows from reading her syllabus in math class that the average of her chapter tests accounts for 60% (0.6) of her overall course grade. She also knows that the final exam counts as 40% (0.4) of her overall course grade. Suppose that the student has earned grades of 86%, 92%, 83%, 96%, and 88% on her five chapter tests. (a.) Determine the range of grades that she would need on her final exam to earn an “A” in the class. (Assume that a grade of “A” is obtained if her overall average is 90% or better.) (b.) Determine the range of grades that she would need on her final exam to earn an “B” in the class. (Assume that a grade of “B” is obtained if her overall average is at least 80% but less than 90%.) For exercises 10 and 11, graph the inequality on a graph paper. Your graphs should be neat, with the axes clearly labeled and marked. Staple the paper to the back of this packet when you turn it in. Exercise 10: 𝑥+𝑦 ≤8 Exercise 11: 3𝑥 − 2𝑦 < −6