Algebra 1 Section 4 2 Properties of Inequality

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, The Addition and c are Property real numbers of Inequality or expressions holdssuch for any thatofathe < b, five inequality then a + c < b symbols. + c.

Example 1 x+7<8 x+7– 7<8– 7 x<1

Example 1 x– 5≠ 3 x– 5+5≠ 3+5 x≠ 8

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

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

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

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

Example 3 P r t = I P 0. 07 1 = 0. 07 P ≥ 875 7 P ≥ 87, 500 P ≥ 12, 500 $12, 500 or more must be invested.

Homework: pp. 151 -152