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

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!!!

“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.

Ex 1) Solve and and Method 1: Solve separately Method 2: Solve together and and

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)

“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.

[ 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.”

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

( ) 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)

] [ 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, ∞)

) ( 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, ∞)

[ ] 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]

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

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 [ ]

Target Goals Solve compound inequalities (ex 1-6) Solve absolute value inequalities (ex 3-6)