Section 1-6 Solving Inequalities

a < b a = b a > b b < > a = For any real numbers a and b, exactly one of the following is true a < b a = b a > b b < > a =

Addition and Subtraction Properties of Inequality Let a, b and c represent any real numbers. Addition Property of Inequality If a < b, then a + c < b + c If a > b, then a + c > b + c Adding or subtracting a number to an inequality doesn’t change the order of the inequality Subtraction Property of Inequality If a < b, then a - c < b - c If a > b, then a - c > b - c

1.) Solve: 3a - 15 > 6 Then graph the solution set. Open circle if < or > Closed circle if ≥ or ≤

2.) Solve: 7(7x - 9) ≤ 84 Then graph the solution set. Open circle if < or > Closed circle if ≥ or ≤

Multiplication and Division Multiplying (or dividing) an inequality by a negative number reverses the order of the inequality > < Multiplication and Division Let a, b and c represent any real numbers where: c > 0 (positive) and d < 0 (negative) Multiplication Property of Inequality If a < b then a • c < b • c but if negative a • d > b • d If a > b then a • c > b • c but if negative a • d < b • d

3.) Solve for x: -3x - 4 ≥ 12

4.) Solve

5.) The product of 8 and a number is less than 42. What is the number?

Homework Page 47 Problems: #4-9, 14-21, 27, 29, 35, 36, 41, and 43