Download Course 3

1-7
Solving Equations by
Adding or Subtracting
Warm Up
Problem of the Day
Lesson Presentation
Course 3
Solving Equations by Adding or
1-7 Subtracting
Learn to solve equations using addition and
subtraction.
Learn to solve equations using multiplication
and division.
Course 3
Solving Equations by Adding or
1-7 Subtracting
Vocabulary
equation
inverse operation
Course 3
Solving Equations by Adding or
1-7 Subtracting
An equation is a mathematical sentence that
uses an equal sign to show that two expressions
have the same value. All of these are equations.
3 + 8 = 11
r + 6 = 14
24 = x – 7
100
= 50
2
To solve an equation that contains a variable, find
the value of the variable that makes the equation
true. This value of the variable is called the
solution of the equation.
Course 33
Course
Solving Equations by Adding or
1-7 Subtracting
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.
Course 3
Solving Equations by Adding or
1-7 Subtracting
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.
Course 3
Solving Equations by Adding or
1-7 Subtracting
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.
Course 3
Solving Equations by Adding or
1-7 Subtracting
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.
Course 33
Course
Solving Equations by Adding or
1-7 Subtracting
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.
Course 33
Course
Numbers
Algebra
2+3=5
+4 +4
2+7=9
x=y
x+ z = y + z
Solving Equations by Adding or
1-7 Subtracting
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.
Course 33
Course
Numbers
Algebra
4 + 7 = 11
3 3
4+4= 8
x=y
x z = y  z
Solving Equations by Adding or
1-7 Subtracting
Additional Example 2A: Solving Equations Using
Addition and Subtraction Properties
Solve.
10 + n = 18
10 + n = 18
–10
–10
0+n= 8
n= 8
Check
10 + n = 18
?
10 + 8 = 18
?
18 = 18 
Course 3
Subtract 10 from both sides.
Identity Property of Zero: 0 + n = n.
Solving Equations by Adding or
1-7 Subtracting
Additional Example 2B: Solving Equations Using
Addition and Subtraction Properties
Solve.
p–8=9
p–8=9
+8 +8
p + 0 = 17
p = 17
Check
p–8=9
?
17 – 8 = 9
?
9 = 9
Course 3
Add 8 to both sides.
Identity Property of Zero: p + 0 = p.
Solving Equations by Adding or
1-7 Subtracting
Additional Example 2C: Solving Equations Using
Addition and Subtraction Properties
Solve.
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 
Course 3
Solving Equations by
1-8 Multiplying or Dividing
You can solve a division equation using the
Multiplication Property of Equality.
MULTIPLICATION PROPERTY OF EQUALITY
Words
You can multiply
both sides of an
equation by the
same number, and
the statement will
still be true.
Course 33
Course
Numbers
2•3=6
4• 2•3=4•6
8 • 3 = 24
Algebra
x=y
z x = zy
Solving Equations by
1-8 Multiplying or Dividing
You can solve a multiplication equation using the
Division Property of Equality.
DIVISION PROPERTY OF EQUALITY
Words
You can divide both
sides of an equation
by the same nonzero
number, and the
equation will still be
true.
Course 33
Course
Numbers
4 • 3 = 12
4 • 3 = 12
2
2
12 = 6
2
Algebra
x=y
x=y
z z
Solving Equations by
1-8 Multiplying or Dividing
Additional Example 1A: Solving Equations Using
Division
Solve 6x = 48.
6x = 48
6x = 48
6
6
1x = 6
x=8
Divide both sides by 6.
1•x=x
Check
6x = 48
? 48
6(8) =
Substitute 8 for x.
? 48
48 =

Course 3
Solving Equations by
1-8 Multiplying or Dividing
Additional Example 1B: Solving Equations Using
Division
Solve –9y = 45.
–9y
–9y
–9
1y
y
= 45
= 45
–9
= –5
= –5
Divide both sides by –9.
1•y=y
Check
–9y = 45
–9(–5) ?= 45 Substitute –5 for y.
? 45
45 =

Course 3
Solving Equations by
1-8 Multiplying or Dividing
Additional Example 2: Solving Equations Using
Multiplication
b = 5.
–4
b = –4 • 5
–4 • –4
b = –20
Solve
Check
Course 3
b =5
–4
–20 =? 5
–4
? 5
5=

Multiply both sides by –4.
Substitute –20 for b.
Solving Equations by
1-8 Multiplying or Dividing
Check It Out: Example 2
c = 5.
–3
c = –3 • 5
–3 • –4
c = –15
Solve
Check
Course 3
c =5
–3
–15 =? 5
–3
? 5
5=

Multiply both sides by –3.
Substitute –15 for c.
Solving Equations by Adding or
1-7 Subtracting
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
Course 3
Solving Equations by
1-8 Multiplying or Dividing
Lesson Quiz
Solve.
1. 3t = 9
t=3
2. –15 = 3b
b = –5
x
3. –4 = –7
x = 28
4. z ÷ 4 = 22 z = 88
5. A roller coaster descends a hill at a rate of 80
feet per second. The bottom of the hill is 400
feet from the top. How long will it take the
coaster rides to reach the bottom?
5 seconds
Course 3