Download Algebra Tiles with Multi

Warm-up:
Solve each equation.
1) 9  2x  17
x=–4
Evaluate each expression.
3)
3  (7)  – 4
12
 4

 12  1212 
2) 6  10  5y
y = –0.8
4) 26  4(7  5)
26  4(2)
18
Simplify each expression
5) 10c  c

11c
6) 8b  4b 12b 0

7) 5m  22m  7
 5m – 4m + 14
m + 14
Solving Multi-Step Equations
Ms. Wooldridge
2012
Multi-Step Equation
Friendship Comparison
You
Just a friend
Best friends
2x 1
7
3
Enemy
Outside the
Crabby Patty


EXAMPLE 1: Solving Multi-Step
Equations
1A)3 2x 1


3
 7  
  3
1 
1 
2x 1  21
–1 –1

2x  20 
–2
–2
x  10

✓ for balance:
2x 1
7
3
2(10) 1
7
3
20 1
7
3
77✓
EXAMPLE 1: Solving Multi-Step
Equations


3x

4
2


2
1B) 1 
 
2 1 
1 

2  3x  4
+4
+4
6  3x
3
3
2x
x 2



✓ for balance:
3x  4
1
2
3(2)  4
1
2
64
1
2
2
1 ✓
2
EXAMPLE 1: Solving Multi-Step
Equations
1C)3 10  2  4 x
 
3
1 

3 
 
1 
30  2  4 x
–2 –2
28  4 x 
–4
–4
7  x
x  7


✓ for balance:
2  4x
10 
3
2  4(7)
10 
3
2  28
10 
3
30
✓
10 
3
EXAMPLE 1: Solving Multi-Step
Equations
2 5k 13 2 
1D)
 1 
 
1  2
1 


✓ for balance:
5k 13
1
2
 11
5k 13  2
5 13
 5 
–13 –13
1

2
5k  11

1113
5
5
1
2 2
11
1
1✓
k     2
2
5
5

Algebra Tiles with Multi-Step Equations
5x  4  3x  4
2x  4  4
5(4)  4  3(4)  4
20  4 12  4
16 12  4
4  4 ✓
x  4
=






Algebra Tiles with Multi-Step Equations
1  5  4x 1 x
1  5  4(1) 1(1)
1  4  3x
1 111
1  x
x 1
1 1 ✓



=
Try these with Algebra Tiles
4x  3  x  2  1
=
x  2
2  3x  2x  3


=
x  1
Try this with algebra tiles:
2(x – 2) – x – 1 = –5
2x  4  x 1  5
x  5  5

=

x 0
EXAMPLE 2: Simplifying Before
Solving Equations
2A) 8x
 21  5x  15
3x  21  15
+21
+21
SIMPLIFY:
Combine like terms
3x  6
3
3
x 2
 ✓ for balance: 8x  21  5x  15
8(2)  21 5(2)  15

16  21 10  15
5 10  15

15  15 ✓
EXAMPLE 2: Simplifying Before
Solving Equations
2B)
4  2a  8  6a
Combine like terms
4  4a  8
–8
–8
4  4a
–4
–4
1 a
a 1
✓ for balance:
4  2(1)  8  6(1)
4 28 6
4  10  6
✓
4

4

EXAMPLE 2: Simplifying Before
Solving Equations
2C) 8 1n
 2  3n  4 Combine like terms
2n 6  4
+6
+6
✓ for
 
 balance:
2n  10
–2 –2
n  5
8  (5)  2  3(5)  4
13  2 15  4
1115  4

44 ✓

EXAMPLE 3: Simplifying Using the
Distributive Property
3A)
5y  2  15
5y 2(5)  15
5y 10  15
+ 10

+ 10
OR
5y 5
5
5
y  1 
5 y  2  15
5
5
y  2  3
+2
+2
y  1
Ex 3A) Check for balance:




5y  2  15
51 2  15
53  15
15  15 ✓
Example where dividing instead of using the
Distributive Property is not best.
6(10x 1)  4x  26
6
6
6
4
26
10x 1 x 
6
6
Best method: Avoid fractions throughout the problem:

6(10x 1)  4x  26
60x  6  4 x  26
64 x  6  26
x  0.5
EXAMPLE 3: Simplifying Using the
Distributive Property
✓ for balance:
3B) 10x 14x  8  20 10(2)  (4(2)  8)  20
10 x 1(4 x) 1(8)
20  (8  8)  20
20  (0)  20
20  20
 20
10x  4 x  8 20
6x  8  20




+
8

+8
6x  12
6
6
x  2
✓


Geometry Application
Write and solve an equation to find the value of x
for each triangle. (Hint: The sum of the angle
measures in any triangle is _____
180 degrees)
1)
85  x 10  2x  5 180
x 10
85

3x  90  180
–90 –90


2x 5


3x  90
3
3
x  30
Geometry Application
Write and solve an equation to find the value of x
for each triangle. (Hint: The sum of the angle
measures in any triangle is _____
180 degrees)
2)
2x  2x  40  180
40
4 x  40  180
–40 –40
2x
2x





4 x  140
4
4
x  35

Solve each equation.
3)

1 
Check your answer.
4w   42

2 

1 
411   42

2 
+2
410.5  42
4w  2  42
+2
4w  44

4
42  42 ✓
4
w  11 

Solve each equation.
4)
Check your answer.
72  x  21
72  5  21
73  21
21  21 ✓
14  7x  21
+ 14
+14
7x  35
7

7
x 5




Solve each equation & check your answer.
5) 5  2x  4
5  ✓ for balance:
 
 2  
2x  4
1  5
1 
2
5
2(3)  4
2x  4  10
2
–4
–4
5


2x  6

64
2
2 2
5
x  3 
22 ✓



Section 2-3 continued on Binder Paper:
6) 7w 12w 11  29
7w 1(2w) 1(11)  29
7w  2w 11  29
5w 11  29


–11
–11
5
5
5w  40
x  8
7(8)  2(8) 11  29
 56  16 11  29
56  27  29
56  27  29
Complete the following practice
problems on binder paper:
Solve each equation.
7)
Check your answer.
4m  7 15
4m  28  15
– 28 – 28
4m 13
4
4
1
m  3
4
 1

43  7 15
 4

 3 
43  15
 4 
15 
4  15 ✓
 4 
Warm-up:
Solve each equation.
1) 11 9x  5
2) 13  10y 18
2
x
3
y = – 0.5
3) 10x  4x  8 
 20
10x  4 x  8  20

6x  8  20
+8
+8
6
6
6x 12

x  2
✓ for balance:
10(2)  (4(2)  8)  20
20  (8  8)  20
20  (0)  20
20  20
✓


Translating Words to an Equation.
Write an equation to represent each relationship. Then solve.
1) Four times the difference of a number and 5,
minus 2 times the number, is equal to –21.
4(n  5) 2n  21
4n  20  2n  21
2n  20  21
2n  1
1


n  0.5 2
 
Translating Words to an Equation.
Write an equation to represent each relationship. Then solve.
2) One-third a number added to quadruple the
sum of the number and two-thirds equals 5.
1
 2 
n  4n  
 3 
3
5
(3) (3)8
(3)1 n 
4n   5(3)
3


3
n 12n  8  15
13n  7

7
n
13
Consecutive Numbers Problem:
5) Joe, Moe, and Bobo’s ages are consecutive
whole numbers. If Joe is the youngest and
Bobo is the oldest. The sum of their ages is
57. Find their ages.
x+1
If Joe = x, then Moe = _____
and Bobo = _____
x+2
x + x + 1 + x + 2 = 57
Joe = 18
3x + 3 = 57 Moe = 19
3x = 54
x = 18 Bobo = 20
Whiteboard Practice:
6) 10  x  2  2x  0
10  x  2  2x  0
12 1x  0
–12
–12
x  12
10  12  2  2(12)  0

10  14  24  0
10  14  24  0

24  24  0
Consecutive Numbers Problems
7) The sum of two consecutive even whole
numbers is 178. What are the two numbers?
If the first even # = x, then the 2nd = x + 2
x + x + 2 = 178
2x + 2 = 178
2x = 176
x = 88
2nd #: 90
8)



Multi-step Equation Practice:
10  7m
 40  42
9
+40
+40
9 10  7m


9
 

2
 
1 
1 
9
10  7m  18
  28
7m
m4
Word Problems Continued…
9) A box of candy bars being sold for D.C. holds
30 bars. If the entire box costs $19.50, how
much is each bar?
n = price of a candy bar
Define the variable: ______________
30n  19.5
Equation: ________________
30
30
n  $0.65 per candy bar
Each bar costs: ____________

Word Problems Continued…
10) The County Fair has an admission fee of $11 and
each ride costs $3.50. If your cousin says he spent
a total of $39, how many rides did he go on?
r = # of rides
Define the variable: ______________
3.5r  39
Equation: 11
________________
-11
-11
3.5r  28
3.5 3.5
Number of rides: ____________
r  8rides