Download Solving One-Step Equations (2-2)

Solving One-Step
Equations (2-2)
Objective: Solve equations by using
addition, subtraction, multiplication, and
division.
Solve Equations Using
Addition or Subtraction
O In an equation, the variable represents the
O
O
O
O
number that satisfies the equation.
To solve an equation means to find the value of
the variable that makes the equation true.
The process of solving an equation involves
isolating the variable (with a coefficient of 1) on
one side of the equation.
Each step in this process results in equivalent
equations.
Equivalent equations have the same solution.
Addition Property of Equality
O If an equation is true and the same number
is added to each side of the equation, the
resulting equivalent equation is also true.
O For any real numbers a, b, and c, if a = b,
then a + c = b + c.
14 = 14
14 + 3 = 14 + 3
17 = 17
-3 = -3
+9 +9
6=6
Example 1
O Solve by adding.
O Horizontal Method:
h – 12 = -27
h – 12 + 12 = -27 + 12
h = -15
O Vertical Method:
h – 12 = -27
+12 +12
h = -15
Check Your Solution:
h – 12 = -27
-15 – 12 = -27
-27 = -27 
Solve Equations Using
Addition or Subtraction
O Similar to the Addition Property of Equality,
the Subtraction Property of Equality can also
be used to solve equations.
Subtraction Property of
Equality
O If an equation is true and the same number
is subtracted from each side of the
equation, the resulting equivalent equation
is also true.
O For any real numbers a, b, and c, if a = b,
then a – c = b – c.
87 = 87
13 = 13
87 – 17 = 87 – 17
-28 -28
70 = 70
-15 = -15
Example 2
O Solve by subtracting.
O Horizontal Method:
c + 102 = 36
c + 102 – 102 = 36 – 102
c = -66
O Vertical Method:
c + 102 = 36
-102 -102
c = -66
Check Your Solution:
c + 102 = 36
-66 + 102 = 36
36 = 36 
Solve Equations Using
Multiplication or Division
O In the equation x/3 = 9, the variable x is
divided by 3.
O To solve for x, undo the division by
multiplying each side by 3.
O This is an example of the Multiplication
Property of Equality.
Multiplication Property of
Equality
O If an equation is true and each side is
multiplied by the same nonzero number, the
resulting equation is equivalent.
O For any real numbers a, b, and c, c ≠ 0, if
a = b, then ac = bc.
O If x = 5, then 3x = 15.
Division Property of Equality
O If an equation is true and each side is
divided by the same nonzero number, the
resulting equation is equivalent.
O For any real numbers a, b, and c, c ≠ 0, if
a = b, then a/c = b/c.
O If x = -20, then x/5 = -20/5 or -4.
O The reciprocal of a number can be used to
solve equations.
Example 3
O Solve each equation.
3
2
1 k 
8
3
8 11
2
8

 k 
11
8
3 11
16
k
33
-75 = -15b
-15
-15
5=b
b=5
4 x
8•4
1 4
x = 32
Example 4
O We can also use reciprocals and properties of
equality to solve real-world problems.
O Ricardo is driving 780 miles to Memphis. He
drove about 3/5 of the distance on the first day.
About how many miles did Ricardo drive?
3
780 
5
3 780
m
5 1
2340
m
5
m
m = 468 miles
Check Your Progress
O Choose the best answer for the following.
O Water flows through a hose at a rate of 5
gallons per minute. How many hours will it
take to fill a 2400-gallon swimming pool?
A.
B.
C.
D.
4h
6h
8h
16 h
m
2400
5
m = 480 minutes
÷ 60
Check Your Progress
O Choose the best answer for the following.
O Solve a – 24 = 16. Then check your solution.
A.
B.
C.
D.
40
-8
8
-40
a – 24 = 16
+24 +24
a = 40
a – 24 = 16
40 – 24 = 16
16 = 16 
Check Your Progress
O Choose the best answer for the following.
O Solve 129 + k = -42. Then check your
solution.
A.
B.
C.
D.
87
-171
171
-87
129 + k = -42
-129
-129
k = -171
129 + k = -42
129 + (-171) = -42
-42= -42 
Check Your Progress
O Choose the best answer for the following.
O Solve  4 1  m  5 3


 3
A.
B.
C.
D.
23
1.
91
2
6.
7
2
1.
21
5
7
3 13
38 3
m
13 3
7 13
114
m
91
Check Your Progress
O Choose the best answer for the following.
O Solve 32 = -14c.
-3
B. 46
C. 18
D. 
. 22
7
A.
32 = -14c
-14 -14
16

c
7