1. Solving Equations by Adding or Subtracting
Course 2 2-3

2. Addition Property of Equality
If you add the same value to each side of an equation, the two sides remain equal.
Arithmetic Algebra
𝟐𝟎 𝟐 = 10, so 𝟐𝟎 𝟐 + 3 = If a = b, then a + c = b + c

3. How to solve an equation
Want to isolate variable (get it alone on one side of the equation)
Can do this by using Inverse Operations

4. Inverse Operations undo each other
Inverse Operations are Operations that Undo each other
Addition and Subtraction are Inverse Operations
Multiplication and Division are Inverse Operations

5. X – 34 = -46 Want to get x alone on 1 side of the equation
What’s in the way of x being alone?

6. X – 34 = -46
34 is on the same side as x
What’s 34 doing to X?

7. X – 34 = -46 34 is being subtracted from x.
How do you undo subtraction?

8. X – 34 = -46 Addition undoes subtraction
So ADD 34 to both sides of the equation
X – =

9. Now Simplify
X – =
X – 0 = -12
X = -12

10. Can Check Solution
Put the solution back into the original equation and see if it is true
X – 34 = substitute -12 for x
-12 – 34
= it is true, so solution is correct

11. Subtraction Property of Equality
If you subtract the same value from each side of an equation, the two sides remain equal.
Arithmetic Algebra
𝟏𝟐 𝟐 = 6, so 𝟏𝟐 𝟐 - 4 = If a = b, then a - c = b - c

12. Solve 114 + m = 249 Want to get m alone on 1 side of the equation
What’s in the way of m being alone?

13. 114 + m = 249 114 is in the way of m being alone.
What is 114 doing to m?

14. 114 + m = 249
114 is being added to m.
How do you undo addition?

15. 114 + m = 249 Subtraction undoes Addition.
So SUBTRACT 114 from both sides of the equation.
114 + m – 114 =

16. Now simplify 114 – 114 + m = 135 Commutative Property of Addition

17. Check Solution
Put the solution back into the original equation and see if it is true
114 + m = 249 substitute 135 for m
= it is true, so solution is correct

18. Golden Rule of Equations…
Golden Rule of Equations…. Do unto the right side as you do unto the left