POINTS TO REMEMBER: The last statement in each item in the preceding set of exercises is the solution set of the given inequality. For example, in no. 4, the solution to 13x + 4 < + 10x consists of all numbers less than (or x < This –5 –3 –3). solution represents all numbers that make the inequality true. The solution can be written using set notation as {x | x < This is read as –3}. the of all numbers x such that x is less than “set –3”. To solve linear inequalities in one variable, isolate the variable that you are solving for on one side of the inequality by applying the properties of inequality. V. Questions/Points to Ponder Observe how the properties of inequality may be used to find the solution set of linear inequalities: 1. b + 14 > 17 b + 14 14 > 17 14 – – b > 3 Solution Set: {b | b > 3} 4t 17 < 51 ‘2. – 4t 17 + 17 < 51 + 17 – 4t < 68 t < 17 Solution Set: {t | t < 17} 2r 32 > 4r + 12 – 2r 32 4r > 4r + 12 4r – – – 32 > 12 –2r – 32 + 32 > 12 + 32 –2r – > 44 –2r r ≤ –22 Solution Set: {r | r < –22} VI. Exercises Find the solution set of the following inequalities. 1. b 19 15 6. 3w + 10 > 5w + 24 – ≤ 2. 9k 7. 12x 40 11x 50 ≤ –27 – ≥ – 3. > 32 8. 7y + 8 < 17 + 4y –2p 4. 3r 5 > 4 9. h 9 < 2(h 5) – – – 5. 2(1 + 5x) < 22 10. 10u + 3 5u > 2u – –18 – VII. Questions/Points to Ponder
POINTS TO REMEMBER: The last statement in each item in the preceding set of exercises is the solution set of the given inequality. For example, in no. 4, the solution to 13x + 4 < –5 + 10x consists of all numbers less than –3 (or x < –3). This solution represents all numbers that make the inequality true. The solution can be written using set notation as {x | x < –3}. This is read as the “set of all numbers x such that x is less than –3”. To solve linear inequalities in one variable, isolate the variable that you are solving for on one side of the inequality by applying the properties of inequality. V. Questions/Points to Ponder Observe how the properties of inequality may be used to find the solution set of linear inequalities: 1. b + 14 > 17 b + 14 – 14 > 17 – 14 b > 3 Solution Set: {b | b > 3} ‘2. 4t – 17 < 51 4t – 17 + 17 < 51 + 17 4t < 68 t < 17 Solution Set: {t | t < 17} 2r – 32 > 4r + 12 2r – 32 – 4r > 4r + 12 – 4r –2r – 32 > 12 –2r – 32 + 32 > 12 + 32 –2r > 44 r ≤ –22 Solution Set: {r | r < –22} VI. Exercises Find the solution set of the following inequalities. 1. b – 19 ≤ 15 6. 3w + 10 > 5w + 24 2. 9k ≤ –27 7. 12x – 40 ≥ 11x – 50 3. –2p > 32 8. 7y + 8 < 17 + 4y 4. 3r – 5 > 4 9. h – 9 < 2(h – 5) 5. 2(1 + 5x) < 22 10. 10u + 3 – 5u > –18 – 2u VII. Questions/Points to Ponder
7-math-lm_mod3.docx