1. Solving Two step equations
Using addition, subtraction, multiplication and division

2. Review
1. x/3 = y-2=17
3. 15=12+ x r=6
5. 14n= x-9+3=4

3. Two Step Equations How do we solve:
Two step equations combine both kinds of one step equations that we have looked at.
Addition or subtraction
Multiplication or division
How do we solve:
Step one= add or subtract
Step two= multiply or divide

4. Example
2x+5=25
Step one: subtract 5 from both sides
Step two: divide by 2 on both sides
2x=20 x= 10 -5 -5
2x=20 2 2

5. Step one: isolate the term containing the variable 2x + 5 = 15 -5 = -5
When we solve two step equations, we want to get the term with the variable alone on one side of the equal sign. Then we want to get the variable alone.
2x + 5 = 15
Step one: isolate the term containing the variable
2x + 5 = 15
-5 = -5
2x = 10
Step two: isolate the variable itself
(1/2)(2 x =10)(1/2)
x= 10(1/2)
x=5
* Remember: Multiplying by ½ is the same thing as dividing by 2 (Inverse Property)

6. Practice 3x + 5 = 17 x – 6 = 10 2 2t + 12 = 54 19 = 4 + 5k x = 4

7. Special Case
In certain cases, you have to multiply or divide first.
Ex. 5 = x+ 2 3
You have to multiply by 3 first, then subtract 2.
15 = x+2
x = 13

8. Equations with Integers
-3x = – y = 9 r = -s 3

9. Positive and Negative Numbers
We solve equations with integers the same way we would solve other equations. The only difference is that we need to pay attention to integer rules.
Ex. -3x = 12
To get x alone, we have to divide by (-3).
-3x = 12
x = -4 why is it negative?

10. Examples: Addition and Subtraction
-5 + y = -7
r + 6 = 4
-12 = k + 4
y = -2
r = -2
k = -16

11. Examples: Mult. And Division
17 = b -3
p = -2
m = 2.095
b = -51

12. Two Step Examples -4x + 3 = -13 6 – y = -4 -3 -3 -4x = -16 6 – 1y = -4
-4x = -16
x = 4
6 – y = -4
When a variable is alone, there is a 1 before it!
6 – 1y = -4
-1y = -10 y = 10