1. Practice sheet 4-1
Go over Homework

2. 4-3 Solving Equations by Adding & Subtracting

3. Equation
An algebraic expression with an equals sign (A complete sentence)
33/x – 2 = 1
x + 3 = 5
4x – 1 = 11

4. Solution
A solution to an equation is any value that makes the equation true.
11 is a solution for
33/x – 2 = 1
2 is a solution for x + 3 = 5
3 is a solution for 4x – 1 = 11

5. Notice the variable is ALWAYS positive
Isolate
Notice the variable is ALWAYS positive
To get a variable alone on one side of the equation.
A = 2
X = 3 - 5
6 = x

6. Addition Property of Equality
When you add the same number/variable to each side of an equation, the two sides remain equal
A = B
A + C = B + C
x - 3 = 5
X = 5 + 3
-1 = 12 –s
-1 +s = 12 – s + s

7. Subtraction Property of Equality
When you subtract the same number/variable to each side of an equation, the two sides remain equal
5(2) = 10
5(2) - 3 =
x + 9 = 5
X = 5 - 9
-11 = 12 + s
-11 - s = 12 + s - s

8. Ch. 4-3 Solving Equations by Adding and Subtracting
To find a solution, isolate the variable, or get it alone on one side.
Use the either the addition or subtraction property of equality depending on the operation in front of the number your are trying to move.
Example: 8 + x = 10 You want to move the eight to get x by itself.
8 + x = 10 The sign in front of the 8 is positive so subtract 8 from both sides.
0 + x = 2
x = 2
For this section we will be talking about addition and subtraction.
Inverse of Addition is ______________
Inverse of Subtraction is _____________
Subtraction
Addition

9. Ch. 4-3 Solving Equations by Adding and Subtracting
Steps to solve equation or isolate the variable:
Move variable if negative by using the addition property of equality
If the number you wish to move is negative use the addition property of equality
If the number you wish to move is positive use the subtraction property of equality
Simplify
Check to see if your answer is correct

10. Solve Addition Equations
Step 2
Use addition property of equality
Step 3
Simplify
Step 4
Check

11. Solving Equations by Adding
Step 2
Undo subtraction by using the addition property of equality
Step 3
Simplify
Step 4
Check

12. Solving Equations by Adding
You always want the variable to be positive
Step 1
Get rid of negative variable by using addition property of equality
Step 2
Get rid of +19 by using subtraction property of equality
Step 3
Simplify
Step 4
Check

13. Solving Equations by Subtracting
Step 2
Undo addition
Step 3
Simplify
Step 4
Check

14. Example 1: Solve each equation below by doing the opposite of the operation shown.
a.) p – 1 = -12 b.) -37 = y – 2
c.) a – 9 = 45 d.) b – 2 = -2
e.) a + 15 = 10 f.) x + 9 = -2
g.) 19 + g = 32 h.) -10 = 3 + c
+1 = +1
p = -11
+2 = +2
-35 = y or y= -35
+2 = +2
b = 0
+9 = +9
a = 54
-15 = -15
a = -5
- 9 = -9
x = -11
= -19
g = 13
-3 = -3
-13 = c or c = -13

15. Example 2: For each equation below determine whether -3 is a solution.
a.) a + 4 = 7 b.) w – 7 = -10
c.) -1 + c = 4 d.) r + 3 = 0
e.) f.)
-3 +4 = 7
1 = 7 No
-3 – 7 = -10
-10 = -10
Yes
-1 -3 = 4
-4 = 4 No
= 0
0 = 0
Yes
3 +2 = 5
5 = -5 No
3= 3
Yes

16. Homework Pg 183 Practice Sheet 4-3 all
#6-20 even(1 pt for work, 1 for answer)
#24 (1 pt for equation, 1 pt for work, 1 pt for answer)
Practice Sheet 4-3 all
(1 pt for work, 1 pt for answer)

19. Example 1: Solve each equation below by doing the opposite of the operation shown.
a.) p – 1 = -12 b.) -37 = y – 2
a + 15 = 10 f.) x + 9 = -2
g.) 19 + g = 32 h.) -10 = 3 + c
-15 = -15
a = -5
- 9 = -9
x = -11
= -19
g = 13
-3 = -3
-13 = c or c = -13

20. Go over Homework Pg 183 #6-20 even(1 pt for work, 1 for answer)
#24 (1 pt for equation, 1 pt for work, 1 pt for answer)

21. Reteach 4-3 Classwork
Homework
Practice Sheet 4-3 all (show work)