Download Algebra_1A_files/Lecture 3-2

Ch 3.2
Objective:
To solve two-step variable equations
Definition
Two Step Equation
Two operations are performed
(1) (+, -) Addition or Subtraction and then
(2) (*, ÷) Multiplication or Division
1) Isolate the variable expression
1) Use Inverse Property of Addition.
(Undo addition with subtraction.
Undo subtraction with addition.)
3) Perform operation to both sides of the equation.
4) Use Inverse Property of Multiplication to isolate
the variable.
(Hint: Multiply by the reciprocal for fractions)
5) Perform operation to both sides of the equation
One-Step Equations
Two-Step Equations
1) m + 2 = 10
-2 -2
m=8
2) 4m + 2 = 10
-2 -2
4m + 0 = 8
4
4
m=2
3) x - 7 = 3
+7 +7
x = 10
4) -2x - 7 = 3
+7 +7
-2x + 0 = 10
-2
-2
x = -5
One-Step Equations
2) 5x + 2 = 37
-2 -2
5x + 0 = 35
5
5
x=7
1) 5x = 35
5 5
x=7
x (-6)
3) (-6) 12 
6
-72 = x

Two-Step Equations

x
4) 11 
1
6
+1
+1
x (-6)
(-6) 12 
6
-72 = x
Solving Equations Involving Fractions
Long Way
3
x9
5
3
3
5
5
3
x9
5
3
x  9
5
9 5
45
x  
1 3
3
x  15
Short Way
5 3 x  9 5 
35
3
9 5
45
x  
1 3
3
x  15
Easier to multiply
by the reciprocal!

Solve.
1) 7 2
7

y  14
2 7
2
14 7
y

1 2
x  49
2) 3 2
 
3
m  18
 2  3
 2 
18 3
m 
1
2
m  27
3) 7
2 7
16  x
2
7 2
7 16

x
2 1
56  x
4) 5 4
5
m9
 4  5
 4 
9 5
m 
1 4
45
1
m
 11
4
5