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.
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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