1. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations METHOD #1 – Inspection Some equations are easy to solve. Ones that have one operation involved and you can “talk” or reason you way thru the answer. An equation is solved ONLY when the unknown has a coefficient of one.

2. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations METHOD #1 – Inspection Some equations are easy to solve. Ones that have one operation involved and you can “talk” or reason you way thru the answer. EXAMPLE # 1 : Solve for “a” : An equation is solved ONLY when the unknown has a coefficient of one.

3. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations METHOD #1 – Inspection Some equations are easy to solve. Ones that have one operation involved and you can “talk” or reason you way thru the answer. EXAMPLE # 1 : Solve for “a” : Something added to 5 equals 12. You could start testing numbers until you get the answer or just “know” the answer will be seven. An equation is solved ONLY when the unknown has a coefficient of one.

4. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations METHOD #1 – Inspection Some equations are easy to solve. Ones that have one operation involved and you can “talk” or reason you way thru the answer. EXAMPLE # 2 : Solve for “a” : Something times ( - 3 ) equals 15. You could start testing numbers until you get the answer or just “know” the answer will be five. An equation is solved ONLY when the unknown has a coefficient of one.

5. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations METHOD #2 – Isolation This method uses opposite operations. You will “isolate” the variable by getting it by itself on one side of the equation and the answer on the other side. An equation is solved ONLY when the unknown has a coefficient of one.

6. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations METHOD #2 – Isolation This method uses opposite operations. You will “isolate” the variable by getting it by itself on one side of the equation and the answer on the other side. OPPOSITE OPERATIONS :ADD - SUBTRACT MULTIPLY - DIVIDE An equation is solved ONLY when the unknown has a coefficient of one.

7. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations METHOD #2 – Isolation This method uses opposite operations. You will “isolate” the variable by getting it by itself on one side of the equation and the answer on the other side. OPPOSITE OPERATIONS :ADD - SUBTRACT MULTIPLY - DIVIDE STEPS : 1. On which side of the equation is my unknown ? 2. If the unknown appears on both sides, you’ll need to get it on one side 3. Move all constants first 4. Move all coefficients last An equation is solved ONLY when the unknown has a coefficient of one.

8. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 1 : Solve

9. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 1 : Solve The left side = the right side. Acts like a seesaw. If I add 10 lbs to one side, I have to add 10 lbs to the other side to keep it balanced. STEPS : 1. On which side of the equation is my unknown ? 2. If the unknown appears on both sides, you’ll need to get it on one side 3. Move all constants first 4. Move all coefficients last Variable is on left side, so I will move things from the left side to the right side…

10. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 1 : Solve STEPS : 1. On which side of the equation is my unknown ? 2. If the unknown appears on both sides, you’ll need to get it on one side 3. Move all constants first 4. Move all coefficients last +8 needs to move, so I will subtract 8 from both sides…

11. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 1 : Solve STEPS : 1. On which side of the equation is my unknown ? 2. If the unknown appears on both sides, you’ll need to get it on one side 3. Move all constants first 4. Move all coefficients last You can see that now we have simplified the left side and our unknown is almost by itself. Remember, to be by itself, it needs to have a coefficient of one…

12. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 1 : Solve STEPS : 1. On which side of the equation is my unknown ? 2. If the unknown appears on both sides, you’ll need to get it on one side 3. Move all constants first 4. Move all coefficients last Our unknown is being multiplied by 2, so we will divide BOTH sides by 2…

13. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 1 : Solve STEPS : 1. On which side of the equation is my unknown ? 2. If the unknown appears on both sides, you’ll need to get it on one side 3. Move all constants first 4. Move all coefficients last Our unknown is being multiplied by 2, so we will divide BOTH sides by 2… ANSWER

14. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 1 : Solve STEPS : 1. On which side of the equation is my unknown ? 2. If the unknown appears on both sides, you’ll need to get it on one side 3. Move all constants first 4. Move all coefficients last Let’s check this answer back into the original equation…

15. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 2 : Solve Variable is on left side, so I will move things from the left side to the right side…

16. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 2 : Solve Place a box around your variable, its coefficient, and any sign that is in front… Another way to attack the first step…

17. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 2 : Solve What do you see outside the box on the same side of the equation ?… Place a box around your variable, its coefficient, and any sign that is in front…

18. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 2 : Solve What do you see outside the box on the same side of the equation ?… Place a box around your variable, its coefficient, and any sign that is in front… ( - 4 )…so ADD 4 to both sides…

19. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 2 : Solve Add 4 to both sides…

20. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 2 : Solve When the coefficient of your unknown is a fraction, multiply both sides by the reciprocal ( flip your fraction )…

21. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 2 : Solve When the coefficient of your unknown is a fraction, multiply both sides by the reciprocal ( flip your fraction )…

22. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve Variable is on right side, so I will move things from the right side to the left side…

23. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve Place a box around your variable, its coefficient, and any sign that is in front…

24. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve What do you see outside the box on the same side of the equation ?…

25. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve What do you see outside the box on the same side of the equation ?… ( + 9 )…so subtract 9 from both sides…

26. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve What do you see outside the box on the same side of the equation ?… ( + 9 )…so subtract 9 from both sides…

27. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve Unknown is being multiplied by ( - 3 ) so we will divide both sides by ( - 3 )

28. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve Unknown is being multiplied by ( - 3 ) so we will divide both sides by ( - 3 )

29. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 3 : Solve Unknown is being multiplied by ( - 3 ) so we will divide both sides by ( - 3 )

30. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve OK, in this example the variable appears on both sides of the equation.

31. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve OK, in this example the variable appears on both sides of the equation. We’ll need to get it on one side so we need to move one of them.

32. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve OK, in this example the variable appears on both sides of the equation. We’ll need to get it on one side so we need to move one of them. I’m going to move the 7x from the right side to the left side…

33. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve Move the 7x from the right side to the left side…

34. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve Move the 7x from the right side to the left side…

35. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve Place a box around your unknown and any coefficient and signs…

36. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve You see +7, so subtract seven from both sides…

37. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve You see +7, so subtract seven from both sides…

38. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve The solution MUST be positive so divide both sides by ( - 1 )…

39. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve The solution MUST be positive so divide both sides by ( - 1 )…

40. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 4 : Solve ANSWER

41. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 5 : Solve

42. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 5 : Solve Get the variables on one side…

43. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 5 : Solve Get the variables on one side…

44. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 5 : Solve Add 11 to both sides…

45. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 5 : Solve Divide both sides by 5…

46. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 5 : Solve You might get a fraction for an answer. Leave improper fractions as improper…

47. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve

48. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve 1 st - distribute

49. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve Subtract 20 from both sides

50. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve Subtract 20 from both sides

51. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve

52. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve

53. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve

54. Linear Equations, Inequalities, and Absolute Value - Solving Linear Equations EXAMPLE 6 : Solve