Drill #10 Solve the following absolute value equalities. Remember to solve for both cases (positive and negative) and check your answers. 1. |2x – 3| = |5 + x| + 2 = |2x – 1| + 6 = – 3

Drill #11 Solve the following absolute value equalities. Remember to solve for both cases (positive and negative) and check your answers. 1. |x + 4| = |2x – 6| + 2 = |2x – 1| + 1 = 10

1-6 Solving Inequalities Objective: To solve inequalities and graph the solution sets.

Calorie Intake 1.Multiply your body weight w by Multiply your height h by Add the numbers 4.Add 655 to your result from step 3 5.Multiply your age a times Subtract the product in step 5 from the expression in step 4

Maintaining body weight The expression for optimal Calorie intake is: 4.3w + 4.7h – 4.7a Multiply by 1.3 to find optimal intake with moderate activity 1.3 (4.3w + 4.7h – 4.7a) How many calories do you need to consume to maintain your weight?

Trichotomy Property Definition: For any two real numbers, a and b, exactly one of the following statements is true: a b A number must be either less than, equal to, or greater than another number.

(1.) Addition and Subtraction Properties For Inequalities* 1.If a > b, then a + c > b + c and a – c > b – c 2.If a < b, then a + c < b + c and a – c < b – c Note: The inequality sign does not change when you add or subtract a number from a side Example: x + 5 > 7

(2.) Multiplication and Division Properties for Inequalities* For positive numbers: 1.If c > 0 and a < b then ac < bc and a/c < b/c 2.If c > 0 and a > b then ac > bc and a/c > b/c For negative numbers: 3.If c < 0 and a < b then ac > bc and a/c > b/c 4.If c b then ac < bc and a/c < b/c

(3.) Non-Symmetry of Inequalities* If x > y then y < x In equalities we can swap the sides of our equations: x = 10, 10 = x With inequalities when we swap sides we have to swap signs as well: x > 10, 10 < x

(4.) Solving Inequalities* solve inequalities the same way as equations (using S. G. I. R.) EXCEPTIONS: Change the inequality sign when you: –multiply or divide by a negative number. – swap sides (non-symmetry property) Example #1*:-4x + 6 > 10 Example #2*:3x > 4x + 2 – x Write your solution in a solution set.

Set Builder Notation** Definition: The solution x < -1 written in set- builder notation: {x| x < -1} We say, the set of all x, such that x is less than -1.

Empty Set** Definition: The set having no members, symbolized by { } or O When an equation has no solution, the answer is said to be null or the empty set.

Classwork 1-6 Study Guide #1-4

Graphing inequalities* Graph one variable inequalities on a number line. get open circles get closed circles For > and > the graph goes to the right.  (if the variable is on the left-hand side) For < and < the graph goes to the left.  (if the variable is on the left-hand side) Example #1*: Graph the solution to the last example

Classwork 1-5 Practice #1-2

Writing Inequalities (#11)* Define a variable and write an inequality for each problem then solve and graph the solution: 4.The product of 11 and a number is less than The opposite of five times a number is less than 321.

Test Scores Ron’s score on the 1 st three of four 100-point chemistry tests were 90, 96, and 86. What must he score on his fourth test to have an average of at least 92 for all the tests?