Solve Inequalities Using Addition and Subtraction Section 6-1 Solve Inequalities Using Addition and Subtraction Objective: Students will create and solve inequalities. Standards: A.REI.1 , A.REI.3 , A.CED.3

Graph of an inequality: The set of points that represent all solutions of the inequality. < or > Open Circle on Graph ≤ or ≥ Closed Circle on Graph

< ≤ > ≥ REVIEW: Fewer than Is less than At most, no more than Symbol Meaning Example < Fewer than Is less than Is less than or equal to ≤ At most, no more than > Is greater than More than Is greater than or equal to ≥ At least, no less than

Example 1 Graph: x < 4 -1 0 1 2 3 4 5 x ≥ -1 -1 0 1 2 3 4 5

Example 2 Write an inequality represented by the graph. -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 x ≤ -1.5 (The inequality points the SAME DIRECTION as the ARROW. But must have variable on LEFT side for this to work!)

Example 3 Solve an inequality using addition: JUSTIFY m – 3.8 < -1 + 3.8 + 3.8 m < 2.8 Graph: -1 0 1 2 3 4 5 6 Given Addition Property of Inequality Simplify

Example 4 Solve an inequality using subtraction: 3 ≤ b + 7 b + 7 ≥ 3 - 7 -7 b ≥ -4 Graph: -5 -4 -3 -2 -1 0 1 2 If variable is on “wrong” side FLIP the WHOLE inequality! Given Symmetric APOI Simplify

Homework Section 6.1 Pg 359 – 361 4 – 8 SOLVE & PROVE: 10, 11, 14- 17, Follow Directions: 31, 32, 34

Solve Inequalities Using Multiplication and Division Section 6-2 Solve Inequalities Using Multiplication and Division Objective: Students will create and solve inequalities. Standards: A.REI.1 , A.REI.3 , A.CED.3

When multiplying or dividing by a NEGATIVE number – you Reverse or Flip the inequality symbol.

< ≤ > ≥ REVIEW: Fewer than Is less than At most, no more than Symbol Meaning Example < Fewer than Is less than Is less than or equal to ≤ At most, no more than > Is greater than More than Is greater than or equal to ≥ At least, no less than

Example 1 Solve an inequality using multiplication: y ≥ -4 y ≥ -28 7 Graph: -34 -32 -30 -28 -26 -24 -22 -20 Given Multiplication Property of Inequality (MPOI) y ≥ -28 Simplify

Example 2 Solve an inequality using multiplication: x > -2 x < 6 -3 -3 • x > -2 • -3 Graph: 0 2 4 6 8 10 12 Given MPOI Flip inequality – multiplied by a negative. x < 6 Simplify

Example 3 ≥ Solve an inequality using division: 18 ≤ -6x x ≤ -3 -6x 18 -6 -6 Graph: -5 -4 -3 -2 -1 0 1 Given SWITCH so x on left side ≥ Symmetric MPOI Flip inequality – divided by a negative. Simplify x ≤ -3

Homework Section 6.2 Pg 366 – 368 Solve & Prove: 3, 7, 11, 15, 19, 23, 30 - 33 Follow Directions: 36, 37, 39