Algebra 1 Section 4.2

Properties of Inequality As with equations, adding or subtracting the same number on both sides of an inequality produces an equivalent inequality, having the same solutions as the original inequality.

Addition Property of Inequality If a, b, and c are real numbers or expressions such that a < b, then a + c < b + c. The Addition Property of Inequality holds for any of the five inequality symbols.

Example 1 x + 7 < 8 x + 7 – 7 < 8 – 7 x < 1

Example 1 x – 5 ≠ 3 x – 5 + 5 ≠ 3 + 5 x ≠ 8

Example 1 -0.6 ≤ x – 0.4 -0.6 + 0.4 ≤ x – 0.4 + 0.4 -0.2 ≤ x x ≥ -0.2

Properties of Inequality What happens if you multiply both sides of an inequality by a positive number? What happens if you multiply both sides of an inequality by a negative number?

Multiplication Property of Inequality If a, b, and c are real numbers or expressions such that a < b, and... 1) c > 0, then ac < bc. 2) c < 0, then ac > bc. The Multiplication Property of Inequality has similar results for >, ≤, or ≥. Remember to reverse the inequality symbol when multiplying or dividing both sides of the inequality by a negative number.

Example 2 -3x < -9 -3x -9 > < -3 -3 x > 3

Example 2 > -4 12 x ( ) 12 > 12(-4) 12 x x > -48

Example 2 - x ≥ 25 2 5 x ( ) (25) 2 5 - ≥ ≤ x ≤ -10

$12,500 or more must be invested. Example 3 P r t = I P 0.07 1 = 0.07P 0.07P ≥ 875 7P ≥ 87,500 P ≥ 12,500 $12,500 or more must be invested.

Homework: pp. 151-152