1. Objectives:
• Students will learn the steps necessary for solving two-step equations.

2. REVIEW

3. Variable: letter that can be used to represent a value
Term: collection of numbers and variables in an expression separated by a plus or minus sign
Algebraic Expressions Terms
a + 2
a, 2
3m + 6n - 6
3m, 6n, - 6
Coefficients: The number part of the terms with variables.
3x + 2y + 7xy + 5
1st term is 3
2nd term is 2
3rd term is 7
Algebraic Expression Coefficient
6m + 5
8r + 7m + 4
14b - 8 6
8, 7 14
Constant: number that cannot change its value
In the expression: 6m + 5, the constant is 5.
In the expression: 8r + 7m + 4
, the constant is 4.
In the expression: 14b - 8
, the constant is - 8.

4. Expression
Equation
5 + 2
= 7 3x
3x = 15
4(5 + 8x)
4(5 + 8x) = - 44

5. terms
5x + 3
constant
coefficient
variable

6. 1. Is 5x2 + x - 7 an expression or equation? expression
2. How many terms are in 5x x - 7?
3 terms
3. List the terms.
5x2 , x , - 7
4. What is the coefficient for 5x2 + x – 7?
First term has coefficient of 5.
Second term has an unwritten coefficient of 1.
5. What is the constant in 5x2 + x - 7 ?
The last term , -7, is called a constant since there is no variable in the term. 6

7. Solving
2 Step
Equations

8. Examples of Two-Step Equations
2. y/4 + 3 = 12
3. 5n + 4 = 6
4. n/2 – 6 = 4

9. Addition  Subtraction Division Multiplication  2 Step Equations
7x + 2 = -54
–5b – 7 = 108
Use inverse operations to get the variable by itself.
Use opposite operations.
Add or subtract first; then multiply or divide.
Addition 
Subtraction
Division
Multiplication 

10. Solving 2 Step Equations
When you do something to one side of the equation
you have to do exactly the same thing on the other side of the equal sign.

11. Solving 2 Step Equations
When you do something to one side of the equation
you have to do exactly the same thing on the other side of the equal sign.
+ 1 +1

12. Solving 2 Step Equations
1. Undo the addition or subtraction operation first, by using inverse operations.
2. Undo the multiplication or division operation second, by using inverse operations.

13. Solving 2 Step Equations
To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations. Inverse Operations are like Opposites.

14. Solving 2 Step Equations
1. GOAL:
Get the variable on one side of the equation.
2. You always perform the same operation to
both sides of an equation.
3. To undo an operation you perform its opposite operation to both sides of the equation.
4. Undo addition or subtraction before you undo multiplication or division.

15. Solving 2 Step Equations
2x + 4 = 10
Get the variable alone.
Subtract 4 from both sides.
2x = 6
__ __
+4 and -4 cancel out
Divide both sides by 2
x = 3
2 divided by 2 cancel to 1
2(3) +4 = 10
Show your check.
6 + 4 = 10
10 = 10
Finish your check.

16. Solving 2 Step Equations
3m - 10 = 17
Get the variable alone.
Add 10 to both sides.
3m = 27
__ __
+10 and -10 cancel out
Divide both sides by 3
m = 9
3 divided by 3 cancel to 1
3(9) – 10 = 17
Show your check.
27 – 10 = 17
Finish your check.
17 = 17

17. Solving 2 Step Equations
x 3
– 4 = 8
Get the variable alone.
Add 4 to both sides.
x 3
= 12
+ 4 and -4 cancel out.
x 3
Multiply both sides by 3.
3 ( ) = 3 12
3 divided by 3 cancel to 1
x = 36
Show your check. 36 3
– 4 = 8
Finish your check.
12 – 4 = 8
8 = 8

18. Solving 2 Step Equations
x 2
+ 6 = 14
Get the variable alone.
Subtract 6 from both sides.
x 2
= 8
+ 6 and -6 cancel out.
x 2
Multiply both sides by 2.
2 ( ) = 2 8
2 divided by 2 cancel to 1
x = 16 16 2
Show your check.
+ 6 = 14
8 + 6 = 14
Finish your check.
14 = 14

19. Solving 2 Step Equations
What Operation Do You Do?
FIRST SECOND
1) 3x + 8 = 24
Divide by 3
Subtract 8
2) 5x - 10 = 19
Divide by 5
Add 10
3) x = 20 2
Add 4
Multiply by 2
4) - 30 = -5x + 5
Divide by -5
Subtract 5

20. Solving 2 Step Equations

21. Solving 2 Step Equations

22. Think about what you need to do to isolate the variable.
Solving 2 Step Equations
Think about what you need to do to isolate the variable.
Get rid of addition or subtraction first. Second get rid of multiplication or division.

23. Are you ready to move on?

24. Try These Examples 2x – 5 = 17 3y + 7 = 25 5n – 2 = 38 12b + 4 = 28

25. Try these examples! x/5 – 3 = 8 x = 55 c/7 + 4 = 9 c = 35 r/3 – 6 = 2
d/9 + 4 = 5
x = 55
c = 35
r = 24
d = 9

26. An Equation is like a balance scale
An Equation is like a balance scale. Everything must be equal on both sides. = 25
2x +5

27. What you do to one side of an equation, you must do to the other side to keep it balanced!= 25
2x +5 -5 -5

28. What you do to one side of an equation, you must do to the other side to keep it balanced!= 20 2x _ 2 __ 2

29. What you do to one side of an equation, you must do to the other side to keep it balanced!= 10 x

30. Try to solve this subtraction equation
How do you get n all by itself? = 18
n - 3 +3 +3

31. Try to solve this subtraction equation
How do you get n all by itself? = 21 n

32. Show your check by substituting your answer back into the original equation.= 18 21
n - 3

33. Try to solve this division equation
How do you get x all by itself? x 3 = •3 •3 15

34. Try to solve this division equation
How do you get x all by itself? x = 45

35. SHOW YOUR CHECK! 45 x 3 = 15

36. Helpful Hints?
Identify what operations are on the variable side. (Add, Sub, Mult, Div)
“Undo” the operation by using opposite operations.
Whatever you do to one side, you must do to the other side of the equal sign to keep equation balanced.