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**Chapter 1.6 Solving Compound & Absolute Value Inequalities**

Algebra 2 Chapter 1.6 Solving Compound & Absolute Value Inequalities Target Goals: Solve compound inequalities Solve absolute value inequalities

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**Compound Inequalities**

2 inequalities joined by “and” or “or” (sometimes with words, sometimes with symbols) 2 Types: “And” Compound Inequalities “Or” Compound Inequalities You will always have 2 inequalities!!!

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**“And” Compound Inequalities**

The compound inequality is true if both of its equalities are true. When looking at the graph, this is where the shading intersects.

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**Ex 1) Solve and and Method 1: Solve separately**

Method 2: Solve together and and

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**Ex 1) Graph the solution set on a number line and express the solution in interval notation.**

-5 6 -5 6 -5 6 Interval Notation: [-5, 6)

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**“Or” Compound Inequalities**

The compound inequality is true if either of its equalities are true. Both don’t have to be true. When looking at the graph, this is wherever the shading naturally falls.

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**[ Ex 2) Solve or Interval Notation: (-∞, -1) or [4, ∞) -1 4 “Solve.”**

4 “Graph the solution set on a number line.” Interval Notation: (-∞, -1) or [4, ∞) “Express the solution in interval notation.”

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**Absolute Value Inequalities**

Absolute value inequality Which compound inequality? Great”or” Less th”and”

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**( ) Interval Notation: (-2, 2)**

Ex 3) Solve Graph the solution set on a number line and express the solution in interval notation. “and” or “or”? 2 inequalities? AND d < 2 and –d < 2 d < 2 and d > -2 ( ) -2 2 Interval Notation: (-2, 2)

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**] [ Interval Notation: (-∞, -3] or [3, ∞) “and” or “or”?**

Ex 4) Solve . Graph the solution set on a number line and express the solution in interval notation. “and” or “or”? 2 inequalities? OR d ≥ 3 or –d ≥ 3 d ≥ 3 or d ≤ -3 ] [ -3 3 Interval Notation: (-∞, -3] or [3, ∞)

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**) ( Interval Notation: (-∞, -3/2) or (5, ∞) “and” or “or”?**

Ex 5) Solve . Graph the solution set on a number line and express the solution in interval notation. “and” or “or”? 2 inequalities? OR 4x – 7 > 13 or -4x + 7 > 13 4x > 20 -4x > 6 x > 5 x < -3/2 x > 5 or x < -3/2 ) ( -3/2 5 Interval Notation: (-∞, -3/2) or (5, ∞)

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**[ ] Interval Notation: [-19/5, 3]**

Ex 6) Solve Graph the solution set on a number line and express the solution in interval notation. “and” or “or”? 2 inequalities? AND 5y + 2 ≤ 17 and –5y – 2 ≤ 17 5y ≤ 15 -5y ≤ 19 y ≤ 3 y ≥ -19/5 [ ] y ≤ 3 and y ≥ -19/5 -19/5 3 Interval Notation: [-19/5, 3]

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**Extention/Challenge ) (**

What type of solution would you have if you have an “and” and no shading intersects on the graph? No solution! ) (

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**Extention/Challenge [ ]**

What type of solution would you have if you have an “or” and the entire line has been shaded? Infinitely many solutions or all real numbers [ ]

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**Target Goals Solve compound inequalities**

(ex 1-6) Solve absolute value inequalities (ex 3-6)

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