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Journal – Graphing Systems of Linear Inequalities Graph each system of inequalities. Remember to double-shade the solution area. Check if each ordered pair is in the solution set. a. 1 y < x+3 3 1 y > − x−2 2 (-6, 1) __ b. x < 2 y<3 (2, 3) (0, 0) (0, 3) (2, 0) (-2, -2) (0, 0) __ (0, 3) __ (0, -2) __ __ __ __ __ __ c. y ≥ 2 x − 4 2 x + 3 y < 12 (0, 0) (3, 2) (0, 4) (0, -4) (2, 2) __ __ __ __ __ Practice Writing Linear Inequalities Symbol Verbal Description Graph, Endpoint and Line Type Examples His wage is less than $8 per hour. < Less than > Greater than ≤ ≥ ≠ = − = 𝟐𝟐 ∗ = 𝟑𝟑 ∗ Open Endpoint ------ Dashed Line 𝒘𝒘 < 𝟖𝟖 She works more than 20 hours per week. • • • Less than or equal to Not more than At most • Greater than or equal to At least • Open Endpoint Closed Endpoint Closed Endpoint ------ ____ ____ Dashed Line 𝒉𝒉 > 𝟐𝟐𝟐𝟐 To order the kids’ meal, you must be not more than 12 years old. Solid Line 𝒂𝒂 ≤ 𝟏𝟏𝟏𝟏 You must be 18 or older to vote. You must be at least 18 years old to vote. Solid Line 𝒂𝒂 ≥ 𝟏𝟏𝟏𝟏 I can meet you anytime except 2pm. Not equal to Open Endpoint 9 Equal to Closed Endpoint ------ ____ Dashed Line 𝒕𝒕 ≠ 𝟐𝟐 The average test score was 84. Solid Line 𝑻𝑻 = 𝟖𝟖𝟖𝟖 Example 1: Four less than twice a number equals 12. • • • • Less than Subtracted from Twice as many Three times as many Not Applicable (N/A) Not Applicable (N/A) 𝟐𝟐𝟐𝟐 − 𝟒𝟒 = 𝟏𝟏𝟏𝟏 Example 2: Anthony threw the ball 10 feet less than Rufus. Anthony’s throw was 10 feet less than Rufus. 𝒂𝒂 = 𝒓𝒓 − 𝟏𝟏𝟏𝟏 Kenneth scored twice as many points as Andre. Kenneth’s score was twice as much as Andre’s. 𝒌𝒌 = 𝟐𝟐𝟐𝟐