Transcript Solving Two step equations

Using addition, subtraction, multiplication
and division
Review
1. x/3 =5
2. y-2=17
3. 15=12+ x
4. 12r=6
5. 14n=6
6. x-9+3=4
Two Step Equations
 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
Example
2x+5=25
Step one: subtract 5 from both sides
2x+5=25
-5 -5
2x=20
Step two: divide by 2 on both sides
2x=20 x= 10
2 2
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)
* Remember: Multiplying by ½ is
x= 10(1/2) the same thing as dividing by 2
x=5
(Inverse Property)
Practice
3x + 5 = 17
x=4
2t + 12 = 54
t = 21
x – 6 = 10
2
x = 32
19 = 4 + 5k
k=3
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
-3x = 12
17 – y = 9
r = -s
3
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
-3 -3
x = -4 why is it negative?
Examples: Addition and Subtraction
 -5 + y = -7
y = -2
r + 6 = 4
r = -2
 -12 = k + 4
k = -16
Examples: Mult. And Division
 2.5p = -5
 - 42m = - 88
 17 = b
-3
p = -2
m = 2.095
b = -51
Two Step Examples
 -4x + 3 = -13
 6 – y = -4
-3
-3
-4x = -16
-4
-4
When a variable is alone,
there is a 1 before it!
x=4
• 6 – 1y = -4
-6
-1y = -10
-1
-1
-6
y = 10