1.  Felicia ate one less than four times the number of cookies Araceli ate. If Felicia ate 11 cookies, how many cookies did Araceli eat? 4a – 1 = 11 4a = 12 a = 3 cookies Twice Araceli One less than twice Araceli 4a– 1

2. 1. X = 5 2. X = 10 3. X = 3.7 4. X = 7.1 5. X = -7 6. X = 7 7. X = -13 8. X = -3 9. X = 7.8 10. x = 4 11. x = 12 12. x = 1 13. x = 6 14. x = 16/5 or 3 1/5 15. x = -3 16. x = -20.83 17. x =.56 18. x = 2 19. x = 16 20. x = 8 21. x = 45/4 or 11 1/4

3. XEI 202: Solve equations in the form x + a = b, where a and b are whole numbers or decimals XEI 302: Solve one-step equations having integer or decimal answers XEI 403: Solve routine first-degree equations

4. 3x = 9 33 In order to isolate “x”, we must get rid of the 3!!! x = 3 9/3 = 3, so x = 3! Check: 3 3 = 9 Yes!!!! Golden Rule: If we divide one side by 3, we must divide the other side by 3!

5. -4x = 20 -4 In order to isolate “x”, we must get rid of the -4!!! x = -5 20/-4 = -5, so x = -5! Check: -4 -5 = 20 Yes!!!! We divide both sides by -4!!!

6. Multiply by the reciprocal! = 5 1 4 x 4 1 4 1 x 1 4.. x = 54 1 x = 20 Follow Golden Rule!

7. Reciprocal Do the same!

8. 1. 5x = 35 2. -3x = 15 3. -6x = 20 4. ½ x = 8 5. 2/5 x = 6 6. ¼ x = 3 1. x = 7 2. x = -5 3. x = 4. x = 16 5. x = 15 6. x = 12

9. XEI 403: Solve routine first-degree equations XEI 404: Perform straightforward word-to-symbol translations XEI 501: Solve real-world problems using first-degree equations

10. Addition & Subtraction x + 7 = 5 – 7 – 7 x = -2 -5 + x = 12 +5 x = 17 Multiplication & Division 6x = 18 6 6 x = 3 2525 5252 2525. x = 8 5252. x = 20

11. 2x + 9 = 15 – 9 2x = 6 2 x = 3 Step #1: Get rid of all addition and subtraction first! Step #2: Get rid of all multiplication and division! To get rid of the +9, you would – 9 on both sides! To get rid of the 2, divide both sides by 2! Check: 2(3) + 9 = 15 6 + 9 = 15 15 = 15

12. -5x – 7 = 13 + 7 -5x = 20 -5 x = -4 Addition and Subtraction first! Check: -5(-4) – 7 = 13 20 – 7 = 13 13 = 13 Multiplication and division second!

13. x + 2 = 8 – 2 x = 6 1 x = 65 Check: 1/5(30) + 2 = 8 6 + 2 = 8 8 = 8 Multiply by the reciprocal! 1515 1515 5151 5151.. x = 30

14. 1. 5x – 9 = 112. -4x + 6 = 22 3. x + 5 = 204. x – 7 = 3 3434 1616 5x = 20 x = 4 -4x = 16 x = -4 3434 x = 15 x = 20 1616 x = 10 x = 60