Transcript pre-algebra 1.3 - Saint John Vianney Catholic School

Solving
Addition
and and
Solving
Addition
1-3
1-3 Subtraction
Equations
Subtraction
Equations
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Warm Up
Write an algebraic expression for each
word phrase.
1.
2.
3.
4.
a number x decreased by 9 x  9
5 times the sum of p and 6 5(p + 6)
2 plus the product of 8 and n 2 + 8n
the quotient of 4 and a number c 4
c
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Problem of the Day
Janie’s horse refused to do 5 jumps today
and cleared 14 jumps. Yesterday, the horse
cleared 9 more jumps than today. He won 3
first place ribbons. How many jumps did the
horse clear in the two-day jumping event?
37
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Learn to solve equations using addition and
subtraction.
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Vocabulary
equation
solve
solution
inverse operation
isolate the variable
Addition Property of Equality
Subtraction Property of Equality
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
An equation uses an equal sign to show that two
expressions are equal. All of these are equations.
3 + 8 = 11
r + 6 = 14
24 = x – 7
100
= 50
2
To solve an equation, find the value of the
variable that makes the equation true. This value
of the variable is called the solution of the
equation.
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Additional Example 1: Determining Whether a
Number is a Solution of an Equation
Determine which value of x is a solution of the
equation.
x + 8 = 15; x = 5, 7, or 23
Substitute each value for x in the equation.
?
x + 8 = 15
?
5 + 8 = 15
?
13=
15 
Substitute 5 for x.
So 5 is not solution.
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Additional Example 1 Continued
Determine which value of x is a solution of the
equation.
x + 8 = 15; x = 5, 7, or 23
Substitute each value for x in the equation.
?
x + 8 = 15
?
7 + 8 = 15
?
15=
15 
Substitute 7 for x.
So 7 is a solution.
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Additional Example 1 Continued
Determine which value of x is a solution of the
equation.
x + 8 = 15; x = 5, 7, or 23
Substitute each value for x in the equation.
?
x + 8 = 15
?
23 + 8 = 15
?
31=
15 
Substitute 23 for x.
So 23 is not a solution.
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Addition and subtraction are inverse
operations, which means they “undo” each
other.
To solve an equation, use inverse operations
to isolate the variable. This means getting
the variable alone on one side of the equal
sign.
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
To solve a subtraction equation, like y  15 = 7, you
would use the Addition Property of Equality.
ADDITION PROPERTY OF EQUALITY
Words
You can add the
same number to
both sides of an
equation, and
the statement
will still be true.
Pre-Algebra
Numbers
Algebra
2+3=5
+4 +4
2+7=9
x=y
x+ z = y + z
Solving Addition and
1-3 Subtraction Equations
There is a similar property for solving addition
equations, like x + 9 = 11. It is called the
Subtraction Property of Equality.
SUBTRACTION PROPERTY OF EQUALITY
Words
You can subtract
the same number
from both sides of
an equation, and
the statement will
still be true.
Pre-Algebra
Numbers
Algebra
4 + 7 = 11
3 3
4+4= 8
x=y
x z = y  z
Solving Addition and
1-3 Subtraction Equations
Additional Example 2A: Solving Equations Using
Addition and Subtraction Properties
Solve.
A. 10 + n = 18
10 + n = 18
–10
–10
0+n= 8
n= 8
Check
10 + n = 18
?
10 + 8 = 18
?
18 = 18 
Pre-Algebra
Subtract 10 from both sides.
Identity Property of Zero: 0 + n = n.
Solving Addition and
1-3 Subtraction Equations
Additional Example 2B: Solving Equations Using
Addition and Subtraction Properties
Solve.
B. p – 8 = 9
p–8=9
+8 +8
p + 0 = 17
p = 17
Check
p–8=9
?
17 – 8 = 9
?
9 = 9
Pre-Algebra
Add 8 to both sides.
Identity Property of Zero: p + 0 = p.
Solving Addition and
1-3 Subtraction Equations
Additional Example 2C: Solving Equations Using
Addition and Subtraction Properties
Solve.
C. 22 = y – 11
22 = y – 11
+ 11
+ 11
Add 11 to both sides.
33 = y + 0
Identity Property of Zero: y + 0 = 0.
33 = y
Check
22 = y – 11
?
22 = 33 – 11
?
22 = 22 
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Additional Example 3A
A. Jan took a 34-mile trip in her car, and the odometer
showed 16,550 miles at the end of the trip. What was
the original odometer reading?
odometer reading at
the beginning of the
trip
+
miles traveled
Solve:
+
34
x
x + 34 = 16,550
–34
– 34
x + 0 = 16,516
=
=
odometer reading at
the end of the trip
16,550
Subtract 34 from both sides.
x = 16,516
The original odometer reading was 16,516 miles.
Pre-Algebra
Solving Addition and
1-3 Subtraction Equations
Additional Example 3B
B. From 1980 to 2000, the population of a town increased
from 895 residents to 1125 residents. What was the
increase in population during that 20-year period?
initial population
Solve:
895
+
increase in
population
+
895 + n = 1125
–895
– 895
0 + n = 230
n
=
=
1125
Subtract 895 from both sides.
n = 230
The increase in population was 230.
Pre-Algebra
population after
increase
Solving Addition and
1-3 Subtraction Equations
Lesson Quiz
Determine which value of x is a solution of the
equation.
1. x + 9 = 17; x = 6, 8, or 26 8
2. x – 3 = 18; x = 15, 18, or 21 21
Solve.
3. a + 4 = 22 a = 18
4. n – 6 = 39 n = 45
5. The price of your favorite cereal is now $4.25. In
prior weeks the price was $3.69. Write and solve an
equation to find n, the increase in the price of the
cereal. 3.69 + n = 4.25; $0.56
Pre-Algebra