1. Review 1.1-1.5 1.1 Variable Expressions 1.2 Addition and Subtraction 1.3 Multiplication and Division 1.4 Multi-step equations 1.5 Variables on Both Sides

2. 1) Solve r + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

3. - 16 -16 r = -23 -23 + 16 = -7 1) Solve r + 16 = -7 1.Subtract 16 from both sides 2.Simplify vertically 3.Check your answer by substituting your answer back into the problem

4. 3) Solve 8 = m - 3 1.m = 5 2.m = 11 3.m = 24 4.m = 8/3 Answer Now

5. 5) Solve. -x - (-2) = 1 -x + 2 = 1 - 2 - 2 -x = -1 -1 -1 x = 1 -(1) + 2 = 1 1.Eliminate the double sign 2.Subtract 2 from both sides 3.Simplify vertically 4.We haven’t gotten x by itself. It still has a negative sign in front. 5.Divide bot sides by -1 6.Check your answer

6. Solve -y – (-3) = 7 1.y = 10 2.y = 4 3.y = -10 4.y = -4 Answer Now

7. 1) Solve -5t = 60 -5 -5 t = -12 -5(-12) = 60 1.Divide both sides by -5 2.Simplify 3.Check your answer

8. 2) Solve 15 = 6n 6 6 n = 5/2 1.Divide both sides by 6 2.Simplify 3.Check your answer

9. 3) Solve -3v = -129 1.v = -126 2.v = -43 3.v = 43 4.v = 126 Answer Now

10. 4) Solve 4 · · 4 x = -48 1.Clear the fraction – multiply both sides by 4 2.Simplify 3.Check your answer

11. (3/2) · = 18 · (3/2) x = 54/2 x = 27 1.Clear the fraction – multiply both sides by the RECIPRICAL 2.Simplify 3.Check your answer 5) Solve = 18

12. 7) Solve 1.b = -56 2.b = -14 3.b = 14 4.b = 56 Answer Now

13. 1) Solve 2x - 1 = -3 + 1 + 1 2x = -2 2 2 x = -1 2(-1) - 1 = -3 -2 – 1 = -3 1.Add 1 to both sides 2.Simplify 3.Divide both sides by 2 4.Simplify 5.Check your answer

14. + 4 + 4 3 · · 3 x = 36 12 – 4 = 8 2) Solve 1.Add 4 to both sides 2.Simplify 3.Clear the fraction - Multiply both sides by 3 4.Simplify 5.Check your answer

15. 3) Solve 3y – 1 = 8 1.y = 3 2.y = -3 3.y = 4.y = Answer Now

16. 3) Solve d – 4 = 6 + 4 + 4 d = 10 1.Clear the fraction - Multiply both sides by 2 2.Simplify 3.Add 4 to both sides 4.Simplify 5.Check your answer

17. 4) Solve 1.d = -7 2.d = -19 3.d = -17 4.d = 17 Answer Now

18. 5) Solve -3 -3 a = 35 1.Subtract 3 from both sides 2.Simplify 3.Clear the fraction – Multiply both sides by -7 4.Simplify 5.Check your answer

19. 6) Solve 5z + 16 = 51 1.z = -35 2.z = -7 3.z = 35 4.z = 7 Answer Now

20. - 1 - 1 5 · · 5 3x = 15 3 3 x = 5 7) Solve 1.Subtract 1 from both sides 2.Simplify 3.Clear the fraction - Multiply both sides by 5 4.Simplify 5.Divide both sides by 3 6.Simplify 7.Check your answer

21. Key Skills Keep it balanced! Solve 6n + 17 = 5 + 4n – 4n 2n + 17 = 5 – 17 2n = -12 ÷ 2 Subtract 4n from each side of the equal sign. Subtract 17 from each side of the equal sign. Divide by 2 n = – 6

22. Do This Together Keep it balanced! Solve 3x + 19 = 4 + 8x x = 3 Subtract 3x from each side of the equal sign. – 3x 19 = 4 + 5x Subtract 4 from each side of the equal sign. – 4 15 = 5x Divide by 5 ÷ 5

23. Try This Keep it balanced! Solve – 3x – 9 = – 13 – 7x x = – 1 Add 3x to each side of the equal sign. + 7x 4x – 9 = – 13 Add 13 to each side of the equal sign. + 9 4x = – 4 Divide by – 4 ÷ 4

24. Do this together Solve 4b + 3 = 3b + 6 b = 3 Subtract 4b from each side of the equal sign. – 4b 3 = – b + 6 Subtract 6 from each side of the equal sign. – 6 – 3 = – b Divide by – 1 ÷ – 1

25. Two special cases: 6(4 + y) - 3 = 4(y - 3) + 2y 24 + 6y - 3 = 4y - 12 + 2y 21 + 6y = 6y - 12 - 6y - 6y 21 = -12 Never true! 21 ≠ -12 NO SOLUTION! 3(a + 1) - 5 = 3a - 2 3a + 3 - 5 = 3a - 2 3a - 2 = 3a - 2 -3a -2 = -2 Always true! INFINITE SOLUTIONS

26. Let’s try another! 3n + 1 = 7n - 5 -3n -3n 1 = 4n - 5 +5 +5 6 = 4n 4 4 Reduce! 3 = n 2 Check: 3(1.5) + 1 =? 7(1.5) - 5 4.5 + 1 =? 10.5 - 5 5.5 = 5.5

27. Solve: Distribute first. 5 + 2y + 8 = 5y - 15 + 10 Next, combine like terms.2y + 13 = 5y – 5 Now solve. (Subtract 2y.)13 = 3y - 5 (Add 5.)18 = 3y (Divide by 3.)6 = y y = 6 5 + 2(y + 4) = 5(y – 3) + 10

28. 4) 3 - 2x = 4x - 6 3 = 6x - 6 9 = 6x x = 3/2 Steps: Multiply each term by the least common denominator (8) to eliminate fractions. Solve for x. Add 2x. Add 6. Divide by 6.

29. Try a few on your own: 9x + 7 = 3x - 5 8 - 2(y + 1) = -3y + 1 8 - 1 z = 1 z - 7 2 4 x = -2 y = -5 z = 20

30. 1.-3 2. 3. 4.3 What is the value of x if 3 - 4x = 18 + x? Answer Now

31. 4) Solve -7(x - 3) = -7 -7x + 21 = -7 - 21 - 21 -7x = -28 -7 -7 x = 4 -7(4 - 3) = -7 -7(1) = -7 1.Distribute 2.Subtract 21 from both sides 3.Simplify 4.Divide both sides by -7 5.Simplify 6.Check your answer

32. What is the value of x if 3(x + 4) = 2(x - 1)? Answer Now 1.-14 2.-13 3.13 4.14

33. Special Case #1 6) 2x + 5 = 2x - 3 -2x 5 = -3 This is never true! No solutions 1.Subtract 2x from both sides 2.Simplify

34. Special Case #2 7) 3(x + 1) - 5 = 3x - 2 3x + 3 – 5 = 3x - 2 3x - 2 = 3x – 2 -3x -3x -2 = -2 This is always true! Infinite solutions or identity 1.Distribute 2.Combine like terms 3.Subtract 3x from both sides 4.Simplify

35. What is the value of x if -3 + 12x = 12x - 3? 1.0 2.4 3.No solutions 4.Infinite solutions Answer Now

36. Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2? Answer Now 1.-8 2.-2 3.2 4.8