warm-up: solve each equation. 1)2) evaluate each expression. 3)4) simplify each expression 5)6) 7) x...

Warm-up:Solve each equation.1) 2)

Evaluate each expression.

3) 4)

Simplify each expression

5) 6)

7)

92x 17

123 ( 7)12

26 4(7 5)

10c c

x = – 4 y = –0.8

– 4

11c

8b 4b 12b

18

0

6 10 5y

5m 2 2m 7 5m – 4m + 14 m + 14

26 4(2)

12 412

Solving Multi-Step Equations

Ms. Wooldridge2012

Multi-Step EquationFriendship Comparison

2x 13

7Best friends Just a friend

Enemy

You

Outside theCrabby Patty

EXAMPLE 1: Solving Multi-Step Equations

1A) ✓ for balance:

2x 13

7

3

1

3

1

2x 121–1 –1

2x 20–2 –2

x 10

2x 13

7

2( 10)13

7

2013

7

7 7✓


1B) ✓ for balance:

2

1

2

1

2 3x 4+4+4

6 3x33

2 x

13x 42

13(2) 42

16 42

12

2✓

1 3x 42

x 2


1C) ✓ for balance:

3

1

3

1

30 2 4x–2–2

28 4x–4–4

7 x

10 2 4x3

10 2 4( 7)

3

10 2283

10 30

3✓

10 2 4x3

x 7


1D) ✓ for balance:

2

1

2

1

5k 132–13 –13

5k 115 5

5k 132

1

5 11

5

13

21

11132

1

2

21✓

5k 132

1

k 11

5 2

1

5

Algebra Tiles with Multi-Step Equations

5x 4 3x 4

x 4

5( 4) 4 3( 4) 4

20 4 12 4

1612 4

4 4✓

=

2x 4 4

Algebra Tiles with Multi-Step Equations

15 4x 1 x

1 x

15 4(1) 1 (1)

11 11

11

x 1✓

=

14 3x

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

=

x 0

2x 4 x 1 5

x 5 5

EXAMPLE 2: Simplifying BeforeSolving Equations

2A)

✓ for balance:

8x 21 5x 15

3x 21 15+21

SIMPLIFY: Combine like terms

+21

3x 63 3

x 2

8x 21 5x 15

8(2) 21 5(2) 15

16 21 10 15

5 10 15✓

15 15


2B)

✓ for balance:

4 2a8 6a

4 4a8–8

Combine like terms

–8

4 4a–4–4

1a

4 2(1)8 6(1)

4 28 6

4 10 6✓

a 1

4 4


2C)

✓ for balance:

8 n 2 3n 4

2n+6

Combine like terms

+6

2n 10–2 –2

n 5

8 ( 5)2 3( 5) 4

13215 4

1115 4✓

1

6

4

4 4

EXAMPLE 3: Simplifying Using the Distributive Property

3A)

5 y 2 15

5y

2(5)

15

5y 10 15+ 10 + 10

5y 555

y 1

OR

5 y 2 155 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 266 6 6

10x 14

6x

26

6Best method: Avoid fractions throughout the problem:

6(10x 1) 4x 26

60x 6 4x 26

64x 6 26

x 0.5

EXAMPLE 3: Simplifying Using the Distributive Property

✓ for balance: 3B)

10x 4x 8 20

1(4x)

1(8)

20

10x 4x 8 20

+ 8 + 8

6x 1266

10( 2) (4( 2)8) 20

20 ( 88) 20

20 (0) 20

20 20✓

1

10x

6x 8 20

x 2

Geometry ApplicationWrite and solve an equation to find the value of x

for each triangle. (Hint: The sum of the angle measures in any triangle is _____ degrees)

1) 180

85

x 10

2x 5

180

85 x 102x 5

3x 90 180–90 –90

3x 9033

x 30

Geometry ApplicationWrite and solve an equation to find the value of x

for each triangle. (Hint: The sum of the angle measures in any triangle is _____ degrees)

2) 180

2x

40

2x

180

2x 2x 40

4x 40 180–40 –40

4x 14044

x 35

Solve each equation. Check your answer.3)

4 w 1

2

42

4w 2 42+ 2 + 2

4w 4444

w 11

4 11 1

2

42

4 10.5 42

42 42 ✓

Solve each equation. Check your answer.

4)

7 2 x 21

14 7x 21+ 14 +14

7x 3577

x 5

7 25 21

7 3 21

2121 ✓

Solve each equation & check your answer.

5) ✓ for balance:

2x 45

2

5

1

5

1

2x 4 10–4 –4

2x 62 2

x 3

2x 45

2

2(3) 45

2

6 45

2

2 2 ✓

Section 2-3 continued on Binder Paper:

6)

7w 2w 11 29

1(2w)

1( 11)

29

7w 2w 11 29

1

7w

5w 11 29–11 –11

5w 4055

x 8

7( 8) 2( 8) 11 29

56 16 11 29

56 27 29

5627 29

Complete the following practice problems on binder paper:

Solve each equation. Check your answer.7)

4 m 7 15

4m 28 15– 28 – 28

4m 1344

m 31

4

4 31

4 7

15

4 33

4

15

415

4

15 ✓

✓ for balance:

Warm-up:Solve each equation.1) 2)

3)

119x 5y = – 0.5

13 10y 18

x 2

3

10x 4x 8 20

10x 4x 8 20

6x 12

6x 8 20

x 2

10( 2) (4( 2)8) 20

20 ( 88) 20

20 (0) 20

20 20✓

+ 8 + 8

66

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

n 0.5

1

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

3n

4 n 2

3

5

1

3n 4n

8

35

n 12n 8 15

13n 7

(3) (3) (3) (3)

n 7

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.

If Joe = x, then Moe = _____x + 1and Bobo = _____x + 2

x + x + 1 + x + 2 = 573x + 3 = 57

3x = 54x = 18

Joe = 18Moe = 19Bobo = 20

Whiteboard Practice:

6)

10 x 2 2x 0

10 x 22x 0

121x 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 = 1782x + 2 = 178

2x = 176x = 88 2nd #: 90

Multi-step Equation Practice:8)

10 7m9

40 42+40 +40

10 7m9

2

9

1

9

1

10 7m 18

7m 28

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?

Define the variable: ______________

Equation: ________________

Each bar costs: ____________

30n 19.53030

n $0.65

n = price of a candy bar

per candy bar

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?

Define the variable: ______________

Equation: ________________

Number of rides: ____________

11 3.5r 39

r 8rides

r = # of rides

3.5r 28 -11 -11

3.53.5

warm-up: solve each equation. 1)2) evaluate each expression. 3)4) simplify each expression 5)6) 7) x...

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