1. Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE
Audience:
The intended learners are 7th grade pre-algebra students who are learning how to solve equations. It will also serve as a review for 8th grade and higher. The review will prepare students so they can expand on their knowledge of how to solve equations. In both cases the exercises will be helpful learning tools. This could be beneficial for hearing impaired students, as auditory learning is not necessary.
Goals/Standards:
Solving Equations is the basis for almost all algebraic concepts. If students struggle with this area, they will struggle with other areas in math as well. It is important that students have a strong foundation solving equations before they move on to higher levels of math. This concept is introduced in 7th grade and built upon as students progress.
7th grade Michigan Grade Level Content Standards (GLCS): A.FO.07.13
Students are to “…generate and solve linear equations…and interpret solutions”
Michigan GLCS: A1.2.1
High School math students are to, “write equations with one or two variables to represent mathematical or applied situations, and solve”
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2. introduction
Today, in Ms. Stechschulte’s 7th grade class, we will be learning how to solve one-step equations. To navigate through this presentation, click on the arrows and buttons at the bottom of the screen. The arrow labeled ‘NEXT’, will take you to the next slide. The arrow labeled ‘BACK’, will take you back to the previous slide. When you get to the Main Menu, click on the first link to begin the lesson. If you need to go back to the previous lessons to clarify concepts, please do so.
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3. Goal
Your goal is to learn the concept of solving equations so you are successful answering the quiz questions. You must know the concepts well enough to solve two-step equations for tomorrow’s class. When you are finished with the first 2 Lessons, go to Lesson 3 and play the online math games for the remainder of the class period.
Good luck and have fun 
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4. What is an equation?
“An equation is a written statement indicating the equality of two expressions”
It consists of a sequence of symbols that are split into left and right sides joined by an equal sign.
For example, = 6 is an equation.
Left side
Right side
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5. 2x + 3 = 5 Parts of an equation * Remember * Left side Right side
Coefficient: the number that is in front of the x. This means that 2 and x are multiplied.
Variable: the letter you are solving for; it needs to be isolated on one side of the equation. A variable can be any letter.
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6. Main menu Solving equations
Lesson 1: Using adding & subtracting Lesson 2: Using multiplication & division Lesson 3: Online Math Games
Click on the link for Lesson 1 to begin.
When finished with Lesson 1, continue with Lesson 2 then 3.

7. Online math games Hoop Shoot Equation Buster Easy Algebra Equations
Say the ‘2 – steps’: Rags to Riches
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8. Solving Equations is like balancing a scale:
x + 1 = 3
To solve an equation you must get x by itself on one side of the equal sign, while keeping the scale balanced 1 1 1 x 1
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9. Solving Equations is like balancing a scale:
To get x by itself you have to take away (subtract) 1. However, this will cause the scale to become unbalanced, so you also have to take away 1 from the other side of the equal sign. 1 1 x 1 1
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10. Solving Equations is like balancing a scale:
x + 1 = 3
x = 2
After you subtract 1 from both sides of the equal sign, you are left with x = 2 1 1 1 x 1
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11. inverse operation
“Two operations are said to be inverse to each other if one operation undoes the effect of the other operation.”
Addition and Subtraction are inverse operations
Multiplication and Division are inverse operations
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12. Solving equations To solve x – 5 = 3,
Inverse operations must be used when solving equations.
In the previous example we SUBTRACTED to undo the ADDITION to get x by itself.
To solve x – 5 = 3,
what operation must you use to get x by itself?
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13. x – 5 = 3 +5 +5 x = 8 Solving equations To solve
If you said ADDITION you are correct! To undo SUBTRACTION you must ADD.
To solve
x – 5 = 3
+5 +5
x = 8
Add 5 to both sides to keep the equation balanced.
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Begin Quiz 1
MORE EXAMPLES

14. More examples
x + 2 = 4
To solve an equation get rid of whatever is with the variable (x). What you do to one side, you must also do to the other side. 1 1 1 1 1 x 1
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15. Subtract 2 from both sides to keep the scale balanced
More examples
x + 2 = 4
Subtract 2 from both sides to keep the scale balanced 1 1
x = 2 1 1 1
To Quiz 1 x 1
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16. Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve
More examples
Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve
x – 2 = 3
+2 +2
x = 5
Add 2 to both sides to keep the equation balanced.
To Quiz 1
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17. -1 = 7 + x -7 -7 -8 = x x = -8 More examples
-1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve
-1 = 7 + x
-8 = x
x = -8
Subtract 7 from both sides to keep the equation balanced.
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18. Solve x + 4 = 9 A. x = 13 B. x = 5 C. x = 9 Quiz 1 Question 1:
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19. Solve x – 5 = 2 A. x = -3 B. x = 2 C. x = 7 Quiz 1 Question 2:
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20. Solve – 5 = 4 + x A. x = -9 B. x = -1 C. x = 9 Quiz 1 Question 3:
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21. Correct!! Nice Work!
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22. Correct!! Great Job!
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23. Correct!! Fabulous!
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24. Let’s look at another example
Incorrect
Try Again
Let’s look at another example
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25. More examples
x + 2 = 4
To solve an equation get rid of whatever is with the variable (x). What you do to one side, you must also do to the other side. 1 1 1 1 1 x 1
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26. Subtract 2 from both sides to keep the scale balanced
More examples
x + 2 = 4
Subtract 2 from both sides to keep the scale balanced 1 1
x = 2 1 1 1 x 1
To Quiz 1
BACK =

27. Let’s look at another example
Incorrect
Try Again
Let’s look at another example
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28. Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve
More examples
Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve
x – 2 = 3
+2 +2
x = 5
Add 2 to both sides to keep the equation balanced.
To Quiz 1

29. Let’s look at another example
Incorrect
Try Again
Let’s look at another example
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30. -1 = 7 + x -7 -7 -8 = x x = -8 More examples
-1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve
-1 = 7 + x
-8 = x
x = -8
Subtract 7 from both sides to keep the equation balanced.
To Quiz 1

31. What is the inverse operation of MULTIPLICATION?
SOLVING EQUATIONS
What is the inverse operation of MULTIPLICATION?
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32. The answer is… DIVISION
SOLVING EQUATIONS
The answer is… DIVISION
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33. What is the inverse operation of DIVISION?
SOLVING EQUATIONS
What is the inverse operation of DIVISION?
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34. The answer is… MULTIPLICATION
SOLVING EQUATIONS
The answer is… MULTIPLICATION
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35. SOLVING EQUATIONS
When you have an equation with multiplication or division, you will do the inverse operation to solve!
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36. Since 6 and x are multiplied, to solve, we divide by 6.
examples
Since 6 and x are multiplied, to solve, we divide by 6.
6x = 48
x = 8
Divide by 6 on both sides to keep the equation balanced.
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Reminder: When a number is divided by itself, it equals 1.

37. Since x is divided by 4, to solve, we multiply by 4.
examples
Since x is divided by 4, to solve, we multiply by 4.
x = 5 4
(4)x = 5(4)
x = 20
Multiply by 4 on both sides to keep the equation balanced.
To Quiz 2
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MORE EXAMPLES

38. More examples
The inverse operation of MULTIPLICATION is DIVISION, so we divide by 10.
10x = 30
x = 3
Divide by 10 on both sides to keep the equation balanced.
To Quiz 2
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39. x = 3 -5 (-5)x = 3(-5) x = -15 More examples
The inverse operation of DIVISION is MULTIPLICATION, so we multiply by -5.
x = 3 -5
(-5)x = 3(-5)
x = -15
Multiply by -5 on both sides to keep the equation balanced.
To Quiz 2
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** Remember: Negative times a positive = negative

40. -2x = -10 -2 -2 x = 5 More examples
The inverse operation of MULTIPLICATION is DIVISION, so we divide by -2.
-2x = -10
x = 5
Divide by -2 on both sides to keep the equation balanced.
To Quiz 2
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** Remember: Negative times a negative = positive

41. Solve 5x = 35 A. x = 175 B. x = 30 C. x = 7 Quiz 2 Question 1:
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42. Let’s look at another example
Incorrect
Try Again
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43. Correct!! Super!
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44. Solve x = 4 -2 A. x = -8 B. x = 6 C. x = -2 Quiz 2 Question 2:
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45. Let’s look at another example
Incorrect
Try Again
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46. Correct!! Fantastic!
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47. Solve -3x = 6 A. x = 2 B. x = -2 C. x = -18 Quiz 2 Question 3:
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48. Let’s look at another example
Incorrect
Try Again
Let’s look at another example
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49. Correct!! Great Job!
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50. More examples
The inverse operation of MULTIPLICATION is DIVISION, so we divide by 10.
10x = 30
x = 3
Divide by 10 on both sides to keep the equation balanced.
To Quiz 2

51. x = 3 -5 (-5)x = 3(-5) x = -15 More examples
The inverse operation of DIVISION is MULTIPLICATION, so we multiply by -5.
x = 3 -5
(-5)x = 3(-5)
x = -15
Multiply by -5 on both sides to keep the equation balanced.
To Quiz 2
** Remember: Negative times a positive = negative

52. -2x = -10 -2 -2 x = 5 More examples
The inverse operation of MULTIPLICATION is DIVISION, so we divide by -2.
-2x = -10
x = 5
Divide by -2 on both sides to keep the equation balanced.
To Quiz 2
** Remember: Negative times a negative = positive