CHAPTER 1 – EQUATIONS AND INEQUALITIES
1 .6 – SOLVING COMPOUND AND ABSOLUTE VALUE INEQUALITIES
Unit 1 – First-Degree Equations and Inequalities
1.6 – Solving Compound and Absolute Value Inequalities
In this section we will review:
Solving compound inequalities
Solving absolute value inequalities
1.6 – Solving Compound and Absolute Value Inequalities
Compound inequality – consists of two inequalities joined by the word and or the word or. To solve a compound inequality, you must solve each
part of the inequality
The graph of a compound inequality containing and is the intersection of the solution sets of the two inequalities Compound inequalities with and are called
conjunctions Compound inequalities with or are called
disjunctions
1.6 – Solving Compound and Absolute Value Inequalities
A compound inequality containing the word and is true if and only if both inequalities are true Example
x ≥ -1
x < 2
x ≥ -1 and x < 2
1.6 – Solving Compound and Absolute Value Inequalities
Example 1 Solve 10 ≤ 3y – 2 < 19. Graph the solution set on a
number line
1.6 – Solving Compound and Absolute Value Inequalities
The graph of a compound inequality containing or is the union of the solution sets of the two inequalities
A compound inequality containing the word or is true if one or more of the inequalities is true Example
x ≤ 1
x > 4
x ≤ 1 or x > 4
1.6 – Solving Compound and Absolute Value Inequalities
Example 2 Solve x + 3 < 2 or –x ≤ -4. Graph the solution set on a
number line.
1.6 – Solving Compound and Absolute Value Inequalities
HOMEWORKPage 45
#12 – 15, 22 – 25, 32, 40 - 41
1.6 – Solving Compound and Absolute Value Inequalities
Absolute Value InequalitiesExample 1
Solve 3 > |d|. Graph the solution set on a number line
1.6 – Solving Compound and Absolute Value Inequalities
Example 2 Solve 3 < |d|. Graph the solution set on a number
line.
1.6 – Solving Compound and Absolute Value Inequalities
An absolute value inequality can be solved by rewriting it as a compound inequality.
For all real numbers a and b, b > 0, the following statements are true: If |a| < b, then –b < a < b
If |2x + 1| < 5, then -5 < 2x + 1 < 5 If |a| > b, then a > b or a < -b
If |2x + 1| > 5, then 2x + 1 > 5 or 2x + 1 < -5
These statements are also true for ≤ and ≥
1.6 – Solving Compound and Absolute Value Inequalities
Example 3 Solve |2x – 2| ≥ 4. Graph the solution set on a number
line.
1.5 – Solving Inequalities
Example 4 According to a recent survey, the average monthly
rent for a one-bedroom apartment in one city neighborhood is $750. However, the actual rent for any given one-bedroom apartment in the area may vary as much as $250 from the average. Write an absolute value inequality to describe this
situation.
Solve the inequality to find the range of monthly rent.
1.5 – Solving Inequalities
HOMEWORKPage 45
#16 – 21, 26 – 31, 33 – 39