University:
Glendale Community College
Course:
MAT142 | College Mathematics
Academic year:

2022
Views:

50

Pages:

9
Author:

eco13s5

Section 2.3: Linear inequalities Chapter 2: Functions, Linear equations, and inequalities 1) Complete the table Inequality Graph 𝑥 > −3 Interval Notation (−3, ∞) 𝑥≤5 (−∞, 5] −2 ≤ 𝑥 < 2 [−2,2) (2, ∞) 𝑥>2 (−∞, −3] 𝑥 ≤ −3 (−∞, 2) 𝑥<2 (5, ∞) 𝑥>5 𝑥 < −3 (−∞, −3) [−2,5) −2 ≤ 𝑥 < 5 2) Complete the table Inequality Graph 𝑥≥6 Interval Notation [6, ∞) 𝑥<2 (−∞, 2) −4 < 𝑥 < 6 (−4,6) [2, ∞) 𝑥≥2 (−∞, 0) 𝑥<0 [0, ∞) 𝑥≥0 (−∞, 2) 𝑥<2 𝑥>5 (5, ∞) (−2,5] −2 < 𝑥 ≤ 5 Section 2.3: Linear inequalities Chapter 2: Functions, Linear equations, and inequalities 3) Complete the table Inequality Graph 𝑥 > −∞ Interval Notation (−∞, ∞) 𝑥≥5 [5, ∞) −2 < 𝑥 ≤ 2 (−2,2] [2, ∞) 𝑥≥2 [3,10) 3 ≤ 𝑥 < 10 (5,9] 5<𝑥≤9 (−4, ∞) 𝑥 < −4 𝑥 ≤ −6 (−∞, −6] [1,5] 1≤𝑥≤5 Section 2.3: Linear inequalities Chapter 2: Functions, Linear equations, and inequalities 4) Complete the table Inequality Graph 𝑥<∞ Interval Notation (−∞, ∞) 𝑥≥7 [7, ∞) −1 ≤ 𝑥 < 4 [−1,4) (−∞, 1] 𝑥≤1 (−1,2) −1 < 𝑥 < 2 [0,3) 0≤𝑥<3 (−∞, 0] 𝑥≤0 𝑥 > −2 (−2, ∞) [1,7] 1≤𝑥≤7 Section 2.3: Linear inequalities Chapter 2: Functions, Linear equations, and inequalities #5-33: Solve each inequality. Express each answer using an inequality, a graph, and interval notation. 5) 𝑥 + 5 < 10 𝑥<5 (−∞, 5) 6) 𝑦 + 6 < 14 𝑦<8 (−∞, 8) 7) 𝑥 – 4 > 20 𝑥 > 24 (24, ∞) 8) 𝑦 – 15 > 23 𝑦 > 38 (38, ∞) 9) 3𝑥 ≥ 21 𝑥≥7 [7, ∞) 10) 4𝑦 ≥ 28 𝑦≥7 [7, ∞) 11) −6𝑧 ≤ 30 𝑧 ≥ −5 [−5, ∞) 12) −4𝑥 ≤ 48 𝑥 ≥ −12 [−12, ∞) 13) 6𝑥 + 10 < 22 𝑥<2 (2, ∞) 14) 5𝑥 + 18 < 38 𝑥<4 15) 8𝑥 – 19 > 13 𝑥>4 (−∞, 4) (4, ∞) 16) 6𝑧 – 20 > 40 𝑧 > 10 (10, ∞) 17) 15 ≤ 3𝑥 + 18 𝑥 ≥ −1 [−1, ∞) 18) 28 ≤ 2𝑧 + 40 𝑧 ≥ −6 [−6, ∞) 19) −44 ≥ 11𝑥 + 11 𝑥 ≤ −5 (−∞, −5] 20) −32 ≥ 4𝑥 + 16 𝑥 ≤ −12 (−∞, −12] 21) 3(5𝑦 − 4) > 48 𝑦>4 (4, ∞) 22) 2(3𝑦 − 11) > 8 𝑦>5 (5, ∞) 23) −3(2𝑥 − 5) > −9 𝑥<4 (−∞, 4) 24) −7(4𝑥 − 1) > −49 𝑥<2 (−∞, 2) 25) 42 ≤ −3(5𝑧 + 1) 𝑧 ≤ −3 (−∞, −3] 26) 6 ≤ −3(4𝑥 − 30) 𝑥≤7 (−∞, 7] 27) −5 ≤ 𝑥 + 3 < 4 −8 ≤ 𝑥 < 1 [−8,1) 28) −2 < 𝑥 + 4 ≤ 10 −6 < 𝑥 ≤ 6 (−6,6] 29) 7 ≤ 𝑥 − 1 ≤ 10 8 ≤ 𝑥 ≤ 11 [8,11] 30) 3 < 𝑥 − 5 < 15 8 < 𝑥 < 20 31) 15 < 3𝑥 ≤ 21 5<𝑥≤7 32) 24 ≤ 6𝑥 < 48 4≤𝑥<8 (8,20) (5,7] [4,8) 33) 33 ≤ 11𝑥 ≤ 77 3≤𝑥≤7 [3,7] 34) 36 ≤ 9𝑥 < 81 4≤𝑥<9 [4,9)