Warm-up:Solve each equation & check your answer.
1) 2)
34x 5
29
w 3
43
43
x 5143
x 203
623
✔
34203
5
29
29
w 329
✔
29
329
3
Warm-up Continued…
What is the LCD of the following fractions?3) 4)
5)
18,
12,
34
LCD : 8
15,
14,
310
LCD : 20
116,
18,
332
LCD : 32
Solving Two-Step Equations:Algebra Tiles,
Friendship Analogy,& MOREInteractive
Algebra
Creating an Equation & then Undoing It
Creating an Equation: Undoing to Solve:
x 3
2x 6
2x 5 11
2x 5 11(2) (2)5 + + 5 – 5 – 5
2x 62 2
x 3
Equivalent Equations
Show on the whiteboard.
_______________________________________________________________
Equivalent equations have the same solutions.
x 6All of these
have the SAMESOLUTION:
x = 6
Two step equations with algebra tiles:• No need to draw or write these. Just demonstrate with algebra
tiles:
Equation:
2x 1 7
Create ZERO pairs
0 =
x 3
Two step equations with algebra tiles:• No need to draw or write these. Just demonstrate with algebra
tiles:
Equation:
4 3x 2
Create ZERO pairs
x 2
Two step equations with algebra tiles:• No need to draw or write these. Just demonstrate with algebra
tiles:
Equation:
5 3 2x
1 x
x 1
Two-Step Equation Friendship Comparison
9y 5 8Best friend (coefficient)
Just a friend(constant)
You Otherside of
the scale(outside the
party)
3w4
7
Two-Step Equation Friendship Comparison
Best friend(coefficient = ¼)
Just a friend(constant)
YouOtherside of
the scale(outside the
party)
EXAMPLE 1: Solving Two-Step Equations
• Solve each equation.1A) ✓ for balance:
18 4n 10– 10– 10
8 4n44
2 n
n 2
18 4n 10
18 4(2)10
18 810
18 18 ✓
EXAMPLE 1: Solving Two-Step Equations
• Solve each equation.1B) ✓ for balance:
32 2 5x–2–2
30 5x–5–5
x 6
32 2 5x
32 2 5( 6)
32 2 30
32 32 ✓
1C) ✓ for balance:
EXAMPLE 2: Solving Two-Step Equations that Contain Fractions
11m4
20+11+11
m4
9(4) (4)
m 36
11m4
20
11 364
20
11 9 20
20 20✓
EXAMPLE 2: Solving Two-Step Equations that Contain Fractions
• Solve each equation. Method 1:
____________________________
y8
34
54
Multiply by the LCD: CLEAR the fractions.
( )8 ( )8
81
y8
81
34
5481
2 2
y
6
10+6 +6
y 16
EXAMPLE 2: Solving Two-Step Equations that Contain Fractions
• Solve each equation. Method 2:
____________________________
y8
34
54
Use fraction operations
34
34
y8
84
81
81
2
y 16
Circle or * the method you
like the best.
✓ for balance:
y8
34
54
168
34
54
84
34
54
54
54
✓
168
÷2÷2
2A)
Which method should we use?
23w
34
712
EXAMPLE 2: Solving Two-Step Equations that Contain Fractions
✓ for balance:
What LCD should we use for Method #1?
(12)(12) (12)
8w 9 7
23w
34
712
34
912
23w
212
32
32
w 14
8w 2
w 28
14
23
14
34
712
212
34
712
212
912
712
✓
4 3 1–9 –9
8
1
4
2B)________________
Which method should we use?
1315n
83
EXAMPLE 2: Solving Two-Step Equations that Contain Fractions
✓ for balance:
What LCD should we use for Method #1?
(15) (15) (15)
5 3n 40
1315n
83
13
13
15n
93
51
51
n 3(5) 15
3n 45
n 15
1315151
83
13 3
83
223
83
✓
–5 3 5+5 +5
3 3
Practice:
• Solve each equation.1)_____________________ ✓ for balance:
1.5 1.2y 5.7+5.7 +5.7
7.2 1.2y1.21.2
y 6
1.5 1.2y 5.7
1.5 1.2(6) 5.7
1.5 7.2 5.7
1.5 1.5 ✓
2)
Practice: Binder Paper
10 5 n4–5–5
5 n4
(-4)(-4)
n 20
What should you do first?
5 4g 3+ 3+ 3
What should you do first?
0.5x 12 6–12 –12
What should you do first?
6a3
7–6 –6
What would you do second?
(3) (3)
What should you do first?
34
38x 32
32
32
( )8( )8
What should you do first?
27j 17
314
17
17
( )14 ( ) 14