University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

360

Pages:

1
Author:

apallirasbnc4

Mini-Lecture 2.9 Solving Linear Inequalities Learning Objectives: 1. Define linear inequality in one variable, graph solution sets on a number line, and use interval notation. 2. Solve linear inequalities. 3. Solve compound inequalities. 4. Solve inequality applications. 5. Key Vocabulary: inequality, <, < , > , > , addition property of inequality, multiplication property of inequality, at least, no less than, at most, no more than, is less than, is greater than. Examples: 1. Graph each inequality on a number line and write it in interval notation. 3 a) x > -5 b) y < 7 c) − ≥ m d) 2 x> − 2 5 2. Using the addition property of inequality, solve each inequality. Graph the solution set and write it in interval notation. a) x + 7 < 12 b) x – 10 > -3 c) -4z – 2> -5z + 1 d) 18 – 2x < -3x + 24 Using the multiplication property of inequality, solve each inequality. Graph the solution set and write it in interval notation. x 3 y e) −8 ≥ f) 3x < 73 g) 0 < h) − z ≤ 9 5 3 8 Using both properties, solve each inequality. 8 1 ( x + 2) > ( x + 3) i) 3(3x – 16) < 12(x – 2) j) -18(z – 2) > -21z + 24 k) 21 7 3. Solve each inequality. Graph the solution set and write it in interval notation. a) − 5 < t ≤ 0 b) − 12 ≤ 2 x < −8 c) 3 ≤ 4 x − 9 ≤ 7 4. Solve the following. a) Eight more than twice a number is less than negative twelve. Find all numbers that make this statement true. b) One side of a triangle is six times as long as another side and the third side is 8 inches long. If the perimeter can be no more than 106 inches, find the maximum lengths of the other two sides. Teaching Notes: • Remind students to reverse the direction of the inequality symbol when multiplying or dividing by a negative number. • Suggest students keep the coefficient of the variable positive whenever possible. • Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) – 3c) graph answers at end of mini-lectures; 1a) [-5,∞); 1b) (∞,7); 1c) [- 3/2, ∞); 1d) ( -2/5, ∞); 2a) (−∞,5] ; 2b) (7, ∞) ; 2c) (3, ∞) ; 2d) ( −∞,6] ; 2e) ( −∞,−24] ; 2f) (−∞,24 1 ) ; 2g) (0, ∞) ; 3 2h) [−15, ∞) ; 2i) (−8, ∞) ; 2j) [−4, ∞) ; 2k) ( 7/5, ∞); 3a) (−5,0] ; 3b) [-6,4); 3c) [3,4]; 4a) x<-10; 4b) 14, 84