Download 3.3 Solving Multi-Step Equations

3.3 Solving Multi-Step
Equations
• To use two or more steps to solve equations.
Solving a Linear Equation
• Sometimes solving a Linear Equation can require
using more then one step to undo operations
• When solving Multi-Step Linear equations, make
sure you Simplify each side of the equation (each
expression) if needed before undoing any
operations.
Ex 1: Multi Step
w/Multiplication
3x + 7 = -8
3x + 7- 7 = -8- 7
3x = -15
3x -15
=
3
3
x = -5
CHECK!
3x + 7 = -8
3(-5) + 7 = - 8
-15 + 7 = -8
-8 = -8
True!
-5 is a solution to this equation!
Now You Try…
1. 6x – 15 = 9
x=4
2. –4 + 7x = –11
x = -1
3. 1 = 5 + 2y
-2 = y
4. –3x + 1 = –8
x=3
Ex 2: Multi Step w/Division
t
+ 21 = 14
8
t
+ 21- 21 =14 - 21
8
t
= -7
8
t
(8) = -7(8)
8
t = -56
Ex 2B: Multi Step w/Division
p -15
= -6
9
p -15
= -6 ( 9)
( 9)
9
p -15 = -54
p -15+15 = -54 +15
p = -39
Since the entire left side is
being divided by 9, I have to
undo that operation first!
Compare…
t
+ 21 = 14
8
t
+ 21- 21 =14 - 21
8
t
= -7
8
t
(8) = -7(8)
8
t = -56
p -15
= -6
9
p -15
= -6 ( 9)
( 9)
9
p -15 = -54
p -15+15 = -54 +15
p = -39
You Try!
1.
3.
z
-14 = 5
2
x
12 = 5 3
2.
4.
q +16
-10 =
-5
24 + x
-8 =
-3
Ex 3: Multi Step w/Fraction
2
-21- q =11
3
2
-21- q + 21 =11+ 21
3
2
- q = 30
3
æ 3ö 2
æ 3ö
ç - ÷ - q = 30 ç - ÷
è 2ø 3
è 2ø
q = -45
Ex 4: Simplify First!
Combine Like
Terms!
7x -3x -8 = 24
4x -8 = 24
4x -8+8 = 24 +8
4x = 32
4x 32
=
4
4
x =8
Check 7x – 3x – 8 = 24!
7x – 3x – 8 = 24
7(8) – 3(8) – 8 = 24
56 – 24 – 8 = 24
24 = 24
TRUE
8 is a Solution!
You Try…
1. 3r – r + 15 = 41
r = 13
2. -8 + 5a – 2 = 20
a=6
3. 13 = 12t – 5 – 3t
2=t
Use the Distributive Property
8 x – 2(x + 7) = 16
8 x – 2(x + 7) = 16
Distribute
8 x – 2x – 14 = 16
Combine Like
Terms
8 x – 2x – 14 = 16
6x – 14 = 16
Undo 6 times
6x = 30
x =5
Undo – 14
Let’s do another…
5x + 3 (x + 4) = 28
5x + 3 (x + 4) = 28
5x + 3x + 12 = 28
8x + 12 = 28
8x + 12 – 12 = 28 – 12
8x = 16
x=
X=2
You Try…
1. 6(x + 2) = 15
x = 1/2
2. 8 – 4(x + 1) = 8
x = -1
3. 3m + 2(m - 5) = 10
m=3