Addition Property of Inequality Exercise Name the property: If a > b, then a + c > b + c. Addition Property of Inequality

Exercise If a > b and c > 0, then ac ___ bc. >

Exercise If a > b and c < 0, then ac ___ bc. <

Exercise Solve x + 3 < 5. x < 2

Exercise Solve – 2x > 8. x < – 4

Properties of Inequalities If a < b, then a + c < b + c. Property 6 < 7 and 6 + 3 < 7 + 3; i.e., 9 < 10 Example

Properties of Inequalities If a < b, then a – c < b – c. Property – 4 < – 2 and – 4 – 5 < – 2 – 5; i.e., – 9 < – 7 Example

Properties of Inequalities If a < b and c > 0, then ac < bc. Property 2 < 5 and 2(3) < 5(3); i.e., 6 < 15 Example

Properties of Inequalities If a < b and c < 0, then ac > bc. Property 2 < 5 and 2(– 3) < 5(– 3); i.e., – 6 > – 15 Example

Properties of Inequalities If a < b and c > 0, then < . a c b c Property 4 < 8 and < ; i.e., 2 < 4 4 2 8 2 Example

Properties of Inequalities If a < b and c < 0, then > . a c b c Property 4 < 8 and ; i.e., – 2 > – 4 4 – 2 8 – 2 > Example

Reverse signs if: multiplying by a negative x 4 – > 10 x < – 40 dividing by a negative – 3x < 6 x > – 2

Example 1 Solve – 4x + 3 > 23, and graph the solution. – 6 – 5 – 4 – 3 – 2 – 1

Example 2 3 4 Solve – x + 8 ≤ 23, and graph the solution. 5 4 3 – – x ≤ 15 3 4 x ≥ – 20

Example 2 3 4 Solve – x + 8 ≤ 23, and graph the solution. x ≥ – 20 – 30 – 20 – 10 10

Example 3 Solve – 2(r + 4) > 19, and graph the solution.

Example 3 Solve – 2(r + 4) > 19, and graph the solution. – 16 – 15 – 14 – 13 – 12

Example 4 Solve 2x ≥ – 2x + 8. 2x + 2x ≥ – 2x + 2x + 8 4x ≥ 8 4 x ≥ 2

Example 5 Solve 3x – 1 < x + 9. 3x – 1 – x < x + 9 – x 2 x < 5

Example 6 Solve 5x – 8 ≤ 9x + 2. 5x – 8 – 9x ≤ 9x + 2 – 9x – 4 x ≥ – 2.5

Example Solve 5x + 3 < – 7. x < – 2

Example Solve – 3x + 5 > 17. x < – 4

Example Solve 2x – 12 < 7x + 13. x > – 5

Example Solve 2(n + 7) > – 3n + 12. n > – 2 5

Example Solve 3(y – 12) < – 2(y – 9) + 1. y < 11

Example Solve 2.5(x – 3) – 3(x – 2.5) > 2x. x < 0

Example Solve 8(0.75x – 0.375) < 12(1.25x + 0.5). x > – 1

Example b 5 Solve + 3 ≥ 12. b ≥ 45

Example b + 3 5 Solve ≥ 12. b ≥ 57

Example a + 3 7 a – 9 5 Solve ≤ . a ≥ 39

Exercise Using the inequality ax – b ≤ c, and assuming that a, b, and c are real numbers with a ≠ 0, solve the inequality for x. Be careful to account for all possible values of a, b, and c.

Exercise x r Using the inequality + s > t, and assuming that r, s, and t are real numbers, solve the inequality for x. Be careful to account for all possible values of r, s, and t.