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