Transcript Solving Multi-Step Equations

PRE-ALGEBRA
Lesson 7-2 Warm-Up
PRE-ALGEBRA
“Solving Multi-Step Equations”
(7-2)
What are the steps for
solving a multi-step
equation?
Step 1: Clear the equation of fractions and decimals. You can clear
decimals by using the decimal that has the most digits after it and moving
all of the decimals that number of jumps to the right.
Example: 0.5a2 + 0.875 = 13.25
Since 0.875 is the greatest number of place values from the end (3),
jump all of the decimals 3 places to the right, so 0.5a2 + 0.875 = 13.25 is
the same as 500a2 + 875 = 13,250
•
•
•
Step 2: Use the Distributive Property to remove parenthesis if you can’t
simplify the problem within them.
Example: 4 (25) = 4 (20 + 5) = 4 • 20 + 4 • 5 = 80 + 20 = 100
Step 3: Combine like terms on each side.
Examples: 4x + 5x = 9x
8a – 5a = 3a
Step 4: “Undo” (since you’re working backwards) addition and
subtraction.
t – 7 + 7 = 20 + 7
Examples: 2x + 5 – 5 = 10 – 5
4
Step 5: Undo multiplication and division.
4 • t = 20
Examples: 2x = 10
• 4
1 4
2
2
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
Example: Solve 2c + 2 + 3c = 12.
2c + 2 + 3c = 12
2c + 3c + 2 = 12
5c + 2 = 12
5c + 2 – 2 = 12 – 2
Commutative Property
Combine like terms
Subtraction Property of Equality
5c = 10
Simplify.
5c
10
=
5
5
Isolate the variable. Use the Division Property of
Equality.
Simplify.
c=2
Check: 2c + 2 + 3c = 12
2(2) + 2 + 3(2) 12
12 = 12
Substitute 2 for c.
The solution checks.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
In his stamp collection, Jorge has five more
than three times as many stamps as Helen. Together
they have 41 stamps. Solve the equation s + 3s + 5 = 41.
Find the number of stamps each one has.
s + 3s + 5 = 41
4s + 5 = 41
Combine like terms.
4s + 5 – 5 = 41 – 5 Subtract 5 from each side.
4s = 36
Simplify.
4s
36
=
4
4
Divide each side by 4.
s=9
Simplify.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
(continued)
Helen has 9 stamps. Jorge has 3(9) + 5 = 32 stamps.
Check: Is the solution reasonable? Helen and Jorge have a total of 41
stamps. Since 9 + 32 = 41, the solution is reasonable.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
Example: Solve 2(3a + 6) + a = 110
6a + 12 + 1a = 110
6a + 1a + 12 = 110
7a + 12 = 110
-12
7a
- 12
= 1498
1
7a
98
=
7
7
1
Distributive Property 
2(3a + 6) = 2 • 3a + 2 • 6
Commutative Property of Addition
(Note: a = 1a  Identity Property)
Combine like terms (3 + 1).
Subtract 12 from each side.
Simplify.
Divide each side by 7.
1
a = 14
Simplify.
Check: 2(3a + 6) + a = 110
2(3 • 14 + 6) + 14
110
2(48) + 14
90
Substitute 14 for a.
110 = 110
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
Solve each equation.
a. 4(2q – 7) = –4
4(2q – 7) = –4
8q – 28 = –4
8q – 28 + 28 = –4 + 28
Use the Distributive Property.
Add 28 to each side.
8q = 24
Simplify.
8q
24
=
8
8
Divide each side by 8.
q=3
Simplify.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
(continued)
b.
44 = –5(r – 4) – r
44 = –5(r – 4) – r
44 = –5r + 20 – r
Use the Distributive Property.
44 = –5r – 1r + 20 Use the Commutative and Associative Properties
of Addition to group like terms.
44 = –6r + 20
Combine like terms (r = 1r by the Identity Property).
44 – 20 = –6r + 20 – 20 Subtract 20 from each side.
24 = –6r
Simplify.
24 –6r
= –6
–6
Divide each side by –6.
–4 = r
Simplify.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
Example: The sum of three consecutive integers is 96. Find
the integers.
Words
sum of three consecutive integers
Let
is
96
=
96
n = the least integer.
Then n + 1 = the second integer,
and n + 2
Equation
= the third integer.
n + n+1 + n+2
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
(continued)
n + (n + 1) + (n + 2) = 96
Equation
(n + n + n) + (1 + 2) = 96
Use the Commutative and
Associative Properties of Addition to
group like terms.
3n + 3 = 96
Combine like terms (n = 1n; 1n + 1n + 1n = 3n).
3n + 3 – 3 = 96 – 3 Subtract 3 from each side.
3n = 93
Simplify.
3n
96
=
3
3
Divide each side by 3.
n = 31
Simplify.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
(continued)
If n = 31, then n + 1 = 32, and n + 2 = 33. The three integers
are 13, 14, and 15.
Check:
Is the solution reasonable? Yes, because
31 + 32 + 33 = 96.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
The sum of three consecutive integers is 42.
Find the integers.
Words
sum of three consecutive integers
Let
is
42
=
42
n = the least integer.
Then n + 1 = the second integer,
and n + 2
Equation
= the third integer.
n + n+1 + n+2
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
(continued)
n + (n + 1) + (n + 2) = 42
(n + n + n) + (1 + 2) = 42
3n + 3 = 42
Use the Commutative and
Associative Properties of Addition to
group like terms.
Combine like terms.
3n + 3 – 3 = 42 – 3 Subtract 3 from each side.
3n = 39
Simplify.
3n
39
=
3
3
Divide each side by 3.
n = 13
Simplify.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Additional Examples
(continued)
If n = 13, then n + 1 = 14, and n + 2 = 15. The three integers
are 13, 14, and 15.
Check:
Is the solution reasonable? Yes, because
13 + 14 + 15 = 42.
PRE-ALGEBRA
Solving Multi-Step Equations
LESSON 7-2
Lesson Quiz
Solve each equation.
1. b + 2b – 11 = 88
33
2. 6(2n – 5) = –90
3. 3(x + 6) + x = 86
–5
17
4. Find four consecutive integers whose sum is –38.
–11, –10, –9, –8
PRE-ALGEBRA