1. Equations - Introduction
Must show ALL steps and ALL work for credit

2. Insert Lesson Title Here
Course 2
1-10
Equations and Their Solutions
Insert Lesson Title Here
Vocabulary
Equation
Solution
Inverse Operation

3. Equations and Their Solutions
Course 2
1-10
Equations and Their Solutions
Ella has 22 CDs. This is 9 more than her
friend Kay has.
This situation can be written as an equation.
An equation is a mathematical statement
that two expressions are equal in value.
An equation is like a balanced scale.
Number of
CDs Ella has 22
is equal to =
9 more than
Kay has
j + 9
Left expression
Right expression

4. Equations and Their Solutions
Course 2
1-10
Equations and Their Solutions
Just as the weights on both sides of a balanced scale are exactly the same, the expressions on both sides of an equation represent exactly the same value.
When an equation contains a variable, a value of the variable that makes the statement true is called a solution of the equation.
22 = j j = 13 is a solution because 22 =
22 = j j = 15 is not a solution because 22 
Reading Math
The symbol ≠ means “is not equal to.”

5.  Equations and Their Solutions 1-10
Course 2
1-10
Equations and Their Solutions
Additional Example 1A: Determining Whether a Number is a Solution of an Equation
Determine whether the given value of the variable is a solution of t + 9 = 17. 26
t + 9 = 17
= 17 ?
Substitute 26 for t.
35 = 17 ? 
26 is not a solution of t + 9 = 17.

6.  Equations and Their Solutions 1-10
Course 2
1-10
Equations and Their Solutions
Additional Example 1B: Determining Whether a Number is a Solution of an Equation
Determine whether the given value of the variable is a solution of t + 9 = 17. 8
t + 9 = 17
8 + 9 = 17 ?
Substitute 8 for t.
17 = 17 ? 
8 is a solution of t + 9 = 17.

7. Solving Two-Step Equations
Course 2
12-1
Solving Two-Step Equations
Learn to solve one-step equations.
Sections 1.11 and 1.12 in textbook.

8. How to solve one-step equations
1. Goal – Get the variable alone
2. Use the inverse operation to undo
On BOTH sides of the equation
Addition and Subtraction are inverse operations
Multiplication and Division are inverse operations
**Remember – Whatever you do to one side you MUST do to the other side!!!

9. 2-Column Notes -2 -2 Step 2 b = 4 Step 3 Check 4 + 2 = 6 Step 4
Example #1
b + 2 = Step 1
Step 2
b = Step 3
Check
4 + 2 = 6 Step 4
6 = 6 Step 5
Instructions – STEPS
Copy Problem
Inverse Operation on BOTH sides
*Do the Math!!!!
Solution – Box –in
Check Answer
Rewrite equation with
Value substituted
5) Do Math and check BOTH sides

10. 2-Column Notes +36 +36 Step 2 n = 53 Step 3 Check 53–36 = 17 Step 4
Example #2
n – 36 = Step 1
Step 2
n = Step 3
Check
53–36 = 17 Step 4
17 = 17 Step 5
Instructions – STEPS
Copy Problem
Inverse Operation on BOTH sides
*Do the Math!!!!
Solution – Box –in
Check Answer
Rewrite equation with
Value substituted
5) Do Math and check BOTH sides

11. 2-Column Notes -18 -18 Step 2 j = 76 Step 3 Check 18+76=94 Step 4
Example #3
18 + j = Step 1
Step 2
j = Step 3
Check
18+76=94 Step 4
94 = 94 Step 5
Instructions – STEPS
Copy Problem
Inverse Operation on BOTH sides
*Do the Math!!!!
Solution – Box –in
Check Answer
Rewrite equation with
Value substituted
5) Do Math and check BOTH sides

12. 2-Column Notes Step 2 Step 3 Step 4 Step 5 Example #4 Step 1
Instructions – STEPS
Copy Problem
Inverse Operation on BOTH sides
*Do the Math!!!!
Solution – Box –in
Check Answer
Rewrite equation with
Value substituted
5) Do Math and check BOTH sides

13. 2-Column Notes Step 2 Step 3 Step 4 Step 5 Example #5 Step 1
Instructions – STEPS
Copy Problem
Inverse Operation on BOTH sides
*Do the Math!!!!
Solution – Box –in
Check Answer
Rewrite equation with
Value substituted
5) Do Math and check BOTH sides

14. 2-Column Notes Step 2 Step 3 Step 4 Step 5 Example #6 Step 1
Instructions – STEPS
Copy Problem
Inverse Operation on BOTH sides
*Do the Math!!!!
Solution – Box –in
Check Answer
Rewrite equation with
Value substituted
5) Do Math and check BOTH sides

15. Try on your own
1. r + 6 = -3
3. h/-3 = 12
= q – 8
= -9d

16. Solving Two-Step Equations
Course 2
12-1
Solving Two-Step Equations
When you solve equations that have one
operation, you use an inverse operation to
isolate the variable. You can also use inverse
operations to solve equations that have more
than one operation.
2x + 3 = 23
n + 7 = 15
– –7
– 3 – 3
n = 8
2x = 20
You need to use
another operation
to isolate x.
It is often a good plan to follow the order of
operations in reverse when solving equations
that have more than one operation.

17. Solving Two-Step Equations
Course 2
12-1
Solving Two-Step Equations
Learn to solve two-step equations.

18. Write down the directions to get to Pope High School from Hightower Trail MS parking lot.
Directions to the HS
Explain how to return to Hightower Trail MS.

19. Can you think of any other situations where you have to work backwards??????

20. How can the order of operations help us solve equations????
List the order of operations 1. 2. 3. 4.
Now list it going backwards 1. 2. 3. 4.

21. Additional Example 1A: Solving Two-Step Equations Using Division
Course 2
12-1
Solving Two-Step Equations
Additional Example 1A: Solving Two-Step Equations Using Division
Solve. Check each answer.
9c + 3 = 39
9c + 3 = 39
– 3 –3
Subtract 3 from both sides.
9c = 36 9c 9
= 36
Divide both sides by 9.
c = 4

22. Additional Example 1A Continued
Course 2
12-1
Solving Two-Step Equations
Additional Example 1A Continued
Check.
9c + 3 = 39
9(4) + 3 ? = 39
Substitute 4 for c. ? = ? =
4 is a solution.

23. Solving Two-Step Equations
Course 2
12-1
Solving Two-Step Equations
Reverse the order of operations when solving equations that have more than one operation.
Helpful Hint

24. Solving Two-Step Equations
Course 2
12-1
Solving Two-Step Equations
Check It Out: Example 1A
Solve. Check the answer.
7c + 6 = 48
7c + 6 = 48
– 6 –6
Subtract 6 from both sides.
7c = 42 7c 7
= 42
Divide both sides by 7.
c = 6

25. Solving Two-Step Equations Insert Lesson Title Here
Course 2
12-1
Solving Two-Step Equations
Insert Lesson Title Here
Check It Out: Example 1A Continued
Check.
7c + 6 = 48
7(6) + 6 ? = 48
Substitute 6 for c. ? = ? =
6 is a solution.

26. Additional Example 2A: Solving Two-Step Equations Using Multiplication
Course 2
12-1
Solving Two-Step Equations
Additional Example 2A: Solving Two-Step Equations Using Multiplication
Solve. y 5
6 +
= 21 y 5
6 +
= 21
– –6
Subtract 6 from both sides. y 5
= 15
(5) y 5
= (5)15
Multiply both sides by 5.
y = 75

27. Additional Example 2B: Solving Two-Step Equations Using Multiplication
Course 2
12-1
Solving Two-Step Equations
Additional Example 2B: Solving Two-Step Equations Using Multiplication
Solve. x 7
– 11 = 9 x 7
– 11 = 9
Add 11 to both sides. x 7
= 20 x 7
= (7)20
Multiply both sides by 7.
(7)
x = 140

28. Insert Lesson Title Here
Course 2
12-1
Solving Two-Step Equations
Insert Lesson Title Here
Check It Out: Example 2A
Solve. y 2
8 +
= 48 y 2
8 +
= 48
– –8
Subtract 8 from both sides. y 2
= 40 y 2
= (2)40
Multiply both sides by 2.
(2)
y = 80

29. Insert Lesson Title Here
Course 2
12-1
Solving Two-Step Equations
Insert Lesson Title Here
Check It Out: Example 2B
Solve. x 5
– 31 = 19 x 5
– 31 = 19
Add 31 to both sides. x 5
= 50 x 5
(5)
= (5)50
Multiply both sides by 5.
x = 250

30. Out ticket Show each step and number each step Solve and Check2.