1.6 Solving Compound and Absolute Value Inequalities

Lets look at things you can do with Inequalities 4 < 20You can add the same number to both side of the inequality and not change the sign < < 28 You also subtract from both side with changing the sign 12 – 5 < 28 – 57 < 23

Multiplication and Division are different When you multiply by a positive number the sign stays the same 4 < 204 * 2 < 20 * 28 < 40 But when you multiply or divide by a negative number, the sign changes direction

Compound Inequality Two inequalities joined by and or the word or x x > -2 and x < And it gives an intersection

10 < x and x < 30 Can be written as 10 < x < 30 This shows the space between 10 and

14 < x – 8 < 32 We can add to all the part of the inequality to solve for x 14 < x – 8 < < x – < So 22 < x < 40 to graph the answer Mark 22 and 40 on a line number and shade between the numbers 2240

Solve Add 2 to all the sides

Solve Add 2 to all the sides Then divide by 3

Solve Add 2 to all the sides Then divide by 3 In Set Building Notation {y| }

Solve x + 3 < 2 or – x ≤ - 4 Do the problems By adding -3Multiply by - 1 x < - 1x ≥ 4 Graphing the answer -1 4 Filled in point at 4 Written as x < - 1 orx ≥ 4

Absolute Value Inequalities If the | x | < a number, then it is an and statement. | x | < 5, means x is between – 5 and 5 So | x | < 5 would be written as – 5 < x < 5

Absolute Value Inequalities If the | x | > a number, then it is an or statement. | x | > 5, means x is less then -5 or greater then 5 So | x | > 5 would be written as x 5

Graphing | x | < 5would be graph as -55 | x | > 5 would be graph as -55

Solve | 2x – 2| ≥ 4 2x – 2 ≥ 4 2x – 2 ≤ - 4 add 2 to both sides 2x ≥ 6 2x ≤ - 2 Divide by 2, this will not change the sign direction

Solve | 2x – 2| ≥ 4 2x – 2 ≥ 4 or 2x – 2 ≤ - 4 add 2 to both sides 2x ≥ 6 or 2x ≤ - 2 Divide by 2, this will not change the sign direction x ≥ 3 or x ≤ - 1

Lets work on a few problem together Page #4 and #5 #10 and #11

Homework Page 44 – 45 #15, 19, 21, 24, 27 – 39 odd, 46, 47