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✓
EXAMPLE 1: Solving Multi-Step Equations
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
EXAMPLE 1: Solving Multi-Step Equations
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
EXAMPLE 1: Solving Multi-Step Equations
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
EXAMPLE 2: Simplifying BeforeSolving Equations
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
EXAMPLE 2: Simplifying BeforeSolving Equations
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