1Math KM1 Chapter Solving Equations 2.2 Formulas and Applications 2.3 Applications and Problem Solving 2.4 Sets, Inequalities, & Interval Notation 2.5 Intersections, Unions, and Compound Inequalities 2.6 Absolute Value Equations and Inequalities

1Math KM2 1.1 Solving Equations

1Math KM3 These WORDS mean the same thing in Algebra. 1.1

1Math KM4 TRUE or FALSE or Neither? Is the equation TRUE or FALSE or Neither? 1.1

1Math KM5 Is it a SOLUTION? Determine whether the given number is a solution of the equation. 1.1

1Math KM6 Equivalent Equations have the same solution set. Are these equations Equivalent? and 1.1

1Math KM7 SOLVE: Example

1Math KM8 SOLVE: Example

1Math KM9 SOLVE: Example

1Math KM10 SOLVE: Example

1Math KM11 SOLVE: Example

1Math KM12 SOLVE: Example 6 NO WAY! or 1.1

1Math KM13 SOLVE: Example 7 Always True IDENTITY R 1.1

1Math KM Formulas and Applications

1Math KM15 Solving Literal Formulas 1.2

1Math KM16 Triangle Problem #1 The PERIMETER of a triangle is given by the formula: The formula is solved for P as P is isolated on the left side of the equals sign. Let’s use our laws of equality to rearrange the terms and solve this formula for b. 1.2

1Math KM17 Triangle Problem #1: continued Since the terms a and c are added to b, let’s subtract them from both sides of the equation. Now simplify both sides. Rewrite with b on the left. It is now solved for b. 1.2

1Math KM18 Triangle Problem #2 The AREA of a triangle is given by the formula: The formula is solved for A as A is isolated on the left side of the equals sign. Let’s solve this formula for the altitude (or height) h. 1.2

1Math KM19 Triangle Problem #2: continued Multiply by the LCD to clear the denominator. Now simplify both sides. Keep going, we need to isolate h. 1.2

1Math KM20 Triangle Problem #2: continued Divide both sides by b. Rewrite with h on the left. It is now solved for h. Now simplify. 1.2

1Math KM21 Triangle Problem #3 The sum of the angles of a triangle is 180°. Let’s solve the formula for x. Subtract y and z from both sides. It is now solved for x. 1.2

1Math KM22 Rectangle Probem #1 The AREA of a RECTANGLE is given by: Let’s solve the formula for w. Divide by l. w l Rewrite with w on the left. 1.2

1Math KM23 Rectangle Probem #2 The PERIMETER of a RECTANGLE is given by: Let’s solve the formula for w. Subtract 2l from both sides. Now divide by 2. w l 1.2

1Math KM24 An Electrical Resistance Formula: Solve it for R Multiply by the LCD r 1 r 2 R to clear fractions. Factor out R. Keep going, we need to isolate R. 1.2

1Math KM25 An Electrical Resistance Formula: Solve it for R... continued Divide by (r 1 + r 2 ) to isolate R. It is now solved for R

1Math KM Applications and Problem Solving

1Math KM27 Roof Angles From the side, the roof of a cabin is shaped like a triangle. The largest angle is three times the smallest. The medium angle is 10 degrees more than the smallest. How large are the angles? 1.3

1Math KM28 Consecutive Integers: n, n+1, n+2,... 0Even 1Odd 2Even 3Odd 4Even 5Odd 6Even 7Odd 8Even 9Odd n n+1 n+2 n n+1 n+2 n n+1 n+2 n n+1 n+2 n n+1 n+2 n n+1 n+2 n n+1 n+2 n n+1 n+2 1.3

1Math KM29 Consecutive Even Integers: n, n+2, n+4,... 0Even 1Odd 2Even 3Odd 4Even 5Odd 6Even 7Odd 8Even 9Odd n --- n n n --- n n+4 n --- n n+4

1Math KM30 Consecutive Odd Integers: n, n+2, n+4,... 0Even 1Odd 2Even 3Odd 4Even 5Odd 6Even 7Odd 8Even 9Odd n --- n n n --- n n+4 n --- n n+4

1Math KM31 Consecutive Integer Patterns 1.3 Consecutive Even Integers: n, n+2, n+4,... Consecutive Odd Integers: n, n+2, n+4,... Consecutive Integers: n, n+1, n+2,...

1Math KM32 Consecutive Odd Integers: n, n+2, n+4,... The numbers are 11, 13, and 15. Find three consecutive odd integers such that the sum of twice the first, three times the second, and four times the third is

1Math KM33 A RAISE? Elizabeth was making $4500 per month before the raise! Elizabeth was doing such an awesome job that her boss gave her a 6% raise. Now her monthly salary is $4,770. What was her salary before the raise? 1.3

1Math KM Sets, Inequalities, & Interval Notation ( x,  ) [ x,  ) (x 1, x 2 ) (- , x) (- , x] [x 1, x 2 ] (x 1, x 2 ] [x 1, x 2 ) 1.4

1Math KM35 Notations: Example 1 Words: Set: Roster Set-Builder Algebra: Graph: Interval: Even Integers Greater than

1Math KM36 Notations: Example 2 Words: Set: Roster Set-Builder Algebra: Graph: Interval: Real Numbers Greater than

1Math KM37 Notations: Example 3 Words: Set: Roster Set-Builder Algebra: Graph: Interval: Real Numbers Greater than or equal to

1Math KM38 Notations: Example 4 Words: Set: Roster Set-Builder Algebra: Graph: Interval: Real Numbers between -1 and 4 1.3

1Math KM39 Notations: Example 5 Words: Set: Roster Set-Builder Algebra: Graph: Interval: All numbers less than

1Math KM40 Notations: Example 6 Words: Set: Roster Set-Builder Algebra: Graph: Interval: All numbers less than or equal to

1Math KM41 Notations: Example 6 Words: Set: Roster Set-Builder Algebra: Graph: Interval: All numbers between -2 and 4 inclusive. 1.4

1Math KM42 Graph and Interval Notation Example 1. Graph the solution set and write it in Interval Notation:

1Math KM43 Graph and Interval Notation Example 2. Graph the solution set and write it in Interval Notation: 3 1.4

1Math KM44 Solve, Graph, and Write the solution in Interval Notation

1Math KM45 Solve, Graph, and Write the solution in Interval Notation 4 1.4

1Math KM46 Solve, Graph, and Write the solution in Interval Notation 1.4

1Math KM47 Solve, Graph, and Write the solution in Interval Notation 1.4

1Math KM48 Solve, Graph, and Write the solution in Interval Notation 1.4

1Math KM49 On Craig’s first two chemistry exams he got scores of 95% and 88%. What score, s, does he need on the next exam to keep an average of at least 90%? Keep that Average UP! Craig must score 87% or higher to keep average of at least 90% 1.4

1Math KM Intersections, Unions, and Compound Inequalities

1Math KM51 AND Conjunction of Inequalities: “and” Intersection of Sets:  Venn Diagram 1.5

1Math KM52 OR Disjunction of Inequalities: “or” Union of Sets:  1.5

1Math KM53 Sets: Example 1 Find the following: 1.5

1Math KM54 Sets: Example 2 Find the following: 1.5

1Math KM55 Linear Inequalities

1Math KM56 Linear Inequalities

1Math KM57 Linear Inequalities

1Math KM Absolute Value Equations and Inequalities 1.6

1Math KM59 Always Remember The absolute value function always results in a number that is zero or positive. | x | = negative ? 1.6

1Math KM60 Absolute Value The distance between two points, a and b, on the number line is |a – b| or |b – a|. Determine the distance between -2 and 28 on the number line. 1.6

1Math KM61 Absolute Value: Solve These The absolute value of a (real) number is its distance from zero on the number line. |x| = 8 |x| = 0 |x| =

1Math KM62 The Formal Definition x xx x x 1.6

1Math KM63 Can we simplify? 1.6

1Math KM64 Can we simplify? 1.6

1Math KM65 Can We Solve This ? |2x – 7| =

1Math KM66 How About This One ? |2x+ 4|= |3x-1| 2x+ 4 = 3x-1 2x+ 4 = -(3x-1) or 5 = x2x+ 4 = -3x+1 5x = -3 x = -3/5 1.6

1Math KM67 Try Another ? |2x – 7| = 13 2x - 7 = -132x – 7 = 13 or 2x = -6 2x = 20 x = 10x =

1Math KM68 Isolate the | | first! |8 – x | - 3 = x = 4 8 – x = -4 4 = x x = -12 or |8 – x | = 4 1.6

1Math KM69 What about Inequality? 1. Graph the boundary points. = 3. Shade the TRUE intervals! 2. Test the intervals. T or F 1.6

1Math KM70 Think Simple! | x | = 8 | x | > 8 | x | <

1Math KM71 What about These? | x | > -8 | x | = -8 | x | <

1Math KM72 One Interval or Two? |2x – 7| < x - 7 > -132x – 7 < 13 and 2x > -62x < 20 x < 10x > -3 and [-3, 10] 10-3

1Math KM73 Isolate the Absolute Value and Solve |8 – x | - 3 > |8 – x | > x <-48 - x > 4 or 12 < x4 > x or

1Math KM74 That’s All For Now!

1Math KM75 Where We Left Off Last Class

1Math KM76 reminders for next edit Include a word problem to choose the best medical plan Based on deductible and percentage payment of balance.