1. Let c be any real number. If a = b, then a + c = b + cIf a = b, then a – c = b – c If a = b, then a ( c )= b ( c )If a = b, then a /c = b /c x + 7 – 7 = 22 – 7 x = 15 – 7 = – 7 x = 15 Vertical steps = less writing.

2. + 12 = + 12 2 5 5 Direction: “SOLVE.” this means, WORK BACKWARDS “UNDO” the operations on the x term.. Rules to follow: SIMPLIFY to 1 variable term. You may need to combine like terms, distributive property to remove ( )’s, and Clear Fractions by multiplying both sides by the LCD (least common denominator).

3. – 5 = – 5 -7.2 -7.2 – 45 = – 45 3 3 4 3 +7 = +7 – 16.3 = – 16.3

4. Sect 2.2 Solving using Order of Operations Combining Like Terms in the simplifying stage. 7 + 8x = + 8x – 5 = – 5 7 + 4x = + 4x – 5 = – 5 3 Always move the smallest variable term!

5. Distributive Property in the simplifying stage. + 5x = + 5x + 7 = + 7 8 8

6. 5 To clear fractions, multiply both sides by the LCD. LCD = 6 6 6 6 – 4x = – 4x 8 Two approaches. 5 5 – 4 = – 4 6 4 5252 5252 – 2 = – 2 3

7. To clear fractions, multiply both sides by the LCD. LCD = 12 12 – 9 = – 9 6 To clear decimals, multiply both sides by 10. Every multiplication of 10 moves the decimal one place to the right. We will multiply by 100. – 530 = – 530 120 = 120 All the above examples are Conditional equations…they have a solution. Contradiction Equation. (No solution) Identity Equations. (Have infinite sols.) False Statement No Solution Contradiction Equation True Statement Infinite Solutions Identity Equation

8. Solve for b. h Isolate the b by undoing the operations taking place on the variable b. Solve for W. Remove the terms with no W 1 st. Next isolate the W by undoing the operations taking place on the variable W. – 2L = – 2L 2 2

9. Solve for a. Move the terms and factors that are outside the ( ) ‘s to the other side. Solve for h. Remove the terms with no h 1 st. Next isolate the h by undoing the operations taking place on the variable h. – 917 = – 917 6 6 Since we have – a, add the a to the left and subtract the fraction to the right. a will be isolated.

10. Sect 2.4 Solving Percentage Problems n% = Convert decimals (fractions) to percent and percent to decimal. Fraction to a percentConvert to a percent. Cross multiply and products are equal. Decimal to a percent. Multiply by 100 Convert to a percent. Notice we moved the decimal point 2 places to the right. Percent to a decimal. Drop % and divide by 100 Convert to a decimal. Notice we moved the decimal point 2 places to the left.

11. We will work both techniques…pick your favorite. Not to bad… just like Sect 1.1 and 1.2. What is 11% of 49? The values that associates with the words “is” and “of” Notice we will always cross multiply by the numbers on the diagonal and divide by the 3 rd number!

12. Cross multiply the numbers on the diagonal and divide by the 3 rd number! Calculator !!! Here is where problems may occur! x really needs to multiplied by 0.01 because of the word percent! Cross multiply the numbers on the diagonal and divide by the 3 rd number! Calculator !!!

13. In 2006, there were 300 million people in the United States, and 62.2% of them lived within 5 mi. of a Wal-Mart store. How many people lived with 5mi. of a Wal-Mart store? Any number that represents a TOTAL associates with 100% and is across from 100 in the proportion or associates with “of.” About 1.6 million students who graduated high school went to college. This was 66% of all high school graduates. How many total high school graduates are there? TOTAL is across from 100 in the proportion or associates with “of.”

14. A car dealer lowered the sticker price of a car from $20,830 to $18,955. What percent of the regular price does the sale price represent? What is the percent discount? The total bill was $47.70 that included 6% sales tax. How much was the merchandise before tax? Any number that represents a ORIGINAL PRICE associates with 100% and is across from 100 in the proportion or associates with “of.” What is the percent discount? We have TOTAL and ORIGINAL price…which is the “of”? ORIGINAL price is the “of”? The $47.70 represent the ORIGINAL price + 6% sales tax WAIT a minute! That means our PERCENTAGE is not 6%, 106%!

15. Sect 2.5 Word Problems

18. x Unknown distance = x 3 times the unknown distance = 3x 3x3x How far he biked = 3x How far he had left to go = x

19. Sect 2.5 Word Problems 1 mile Mile x Mile x + 1 First marker = x Next consecutive marker = x + 1 x + x + 1 = 559

20. Sect 2.5 Word Problems Length Width 94 ft by 50 ft

21. Sect 2.5 Word Problems B = Number of brochures to print Starting Cost+ The number of Brochures 2($300) + B(the cost of each Brochures) $600 + B($0.215) Change cents to dollars! Can print 11,162 brochures and not go over budget.

22. Sect 2.5 Word Problems Back side is the unknown = x Peak = 2x Front = x + 20 The sum of three angles of a triangle is 180 degrees. x + 2x + x + 20 = 180 4x + 20 = 180 4x = 160 x = 40

23. Sect 2.5 Word Problems H = the hammer price of final bid. $1150 + 8%(of final bid) = final bid The final bid must be $1250 or higher. Proportion Style. Jared has to pay the Auctioneer 8% of the final bid, so he gets 92% of the final bid.

24. Let A > B and C is a non-zero positive constant. REMEMBER!!!

25. How to write a solution set with set builder notation, interval notation and Graph. Let x > 3 be our solution. We want all x values between -2 and 3. Graph. ( Author.Mr. Fitz Let x < 3 be our solution. ] Author. Mr. Fitz Compound inequalities Let x > – 2 and x < 3 be our solution. ] Author. ( Mr. Fitz “The set of all x, such that x > 3.” { x | x > 3 } Set builder notation REMEMBER! When x is on the left side the inequality symbol points in the direction of the graph. Interval notation

26. Solve the inequalities. Graph the solution and write in interval notation. Flip inequality symbol 4 + 1 – 2x + 1 4 – 2

27. – 6 – 5 – 2x If you move the smallest variable term, it will stay positive. Switch the inequality around so x is on the left side. – 1 5 5 + 5x + 28 8 8

29. $50+$15(per person)< $450 Let p = how many people The party cannot exceed 26 people! – 50 15 Let h = how many hours worked in the 4 th week Average of 4 wks> 16 hours/week 44 – 46 Dina has to work at least 18 hours in the 4 th week.