~ Chapter 2 ~
Solving Equations
Lesson 2-1 Solving One-Step Equations
Lesson 2-2 Solving Two-Step Equations
Lesson 2-3 Solving Multi-Step Equations
Lesson 2-4 Equations with Variables on Both Sides
Lesson 2-5 Equations & Problem Solving
Lesson 2-6 Formulas
Lesson 2-7 Using Measures of Central Tendency
Chapter Review
Solving One-Step Equations
Notes
n/
6
x6
=5
x/
x6
-3
= 18
x (-3) x(-3)
n = 30
x = -54
-a/5 = -20
(-4/1) -1/4m = 8 (-4/1)
x(-5) x(-5)
a = 100
(5 / 2 )
m
8/
15
4/
3
= 2/5a (5/2)
= a
1 1/3 = a
= -32
Solving Two-Step Equations
Notes
Steps for Solving Two-Step Equations
(1) Use the Addition or Subtraction Property of Equality
to get the term with a variable on one side of the
equation.
(2) Use the Mulitplication or Division Property of Equality
to write an equivalent equation in which the variable
has a coefficient of 1.
10 = m/4 + 2
-2
(x4) 8 =
-2 (Step 1)
m/
32 = m
4
(x4)
(Step 2)
Solving Two-Step Equations
Notes
7 = 2y – 3
6a + 2 = -8
x/9 – 15 = 12
Justify steps for solving equations – give reasons for each
step… properties, rules, or definitions…
Solving Two-Step Equations
Homework
Practice 2-1 & Practice 2-2
Odd problems both pages
Solving Multi-Step
Equations
Practice 2-1
Solving Multi-Step Equations
Practice 2-2
Solving Multi-Step Equations
Notes
Steps for Solving Multi-Step Equations
(1) Clear the equation of fractions & decimals.
(2) Use the distributive property if grouping symbols are present.
(3) Combine Like Terms
(4) Subtract or Add using the equality property to isolate the variable.
(5) Divide or Multiply using the equality property to solve for the variable.
Examples…
2c + c + 12 = 78
3x – 4x + 6 = -2
-2y + 5 + 5y = 14
-2(b – 4) = 12
3(k + 8) = 21
15 = -3(x – 1) + 9
Solving Multi-Step
Equations
Notes
Solving an Equation that Contains Fractions
Method 1
Method 2
2x/3 + x/2 = 7
2x/3 + x/2 = 7
2/3 x + ½ x = 7
6(2x/3 + x/2) = 6(7)
4/6 x + 3/6 x = 7
4x + 3x = 42
7/6 x = 7
7x = 42
(6/7) 7/6 x = 7 (6/7)
÷7
x=6
m/4 + m/2 = 5/8
÷7
x=6
2/3 x – 5/8 x = 26
Solving Multi-Step
Equations
Notes
Solving an Equation that Contains Decimals
(Multiply using the equality property to remove the decimals)
0.5a + 8.75 = 13.25
Multiply both sides by?????
100(0.5a + 8.75) = 100 (13.25)
50a + 875 = 1325
50a = 450
a=9
0.025x + 22.95 = 23.65
1.2x – 3.6 + 0.3x = 2.4
Solving Multi-Step
Equations
Homework
Practice 2-3 #1-46
even
Equations with Variables on Both Sides
Practice 2-3
Equations with Variables on Both Sides
Cumulative Review
Equations with Variables on Both Sides
Notes
Use the Addition or Subtraction Properties of Equality to get the variables
on one side of the equation.
Examples
6x + 3 = 8x – 21
Subtract ?
6x + 3 = 8x – 21
– 6x
(Goal is to have the variable on one side of the equation)
– 6x
3 = 2x – 21
+21
(Solve just like 2 step equations)
+21
24 = 2x
÷2
÷2
12 = x
Try these…
or x = 12
2(c – 6) = 9c + 2
c = -2
7k – 4 = 5k + 16
k = 10
Equations with Variables on Both Sides
Notes
-36 + 2w = -8w + w
w=4
An Identity is an equation that is true for every value of the variable.
6x = 6x is an identity.
Identities and Equations with No Solutions
10 – 8a = 2(5 – 4a)
10 – 8a = 10 – 8a
+8a
10
+8a
= 10
This is always true…
Identity
6m – 5 = 7m + 7 – m
6m – 5 = 6m + 7
-6m
-6m
-5 = 7
Not true…
No Solutions
Equations with Variables on Both Sides
Notes
Determine if the following is an identity or an equation with no solution…
14 – (2q + 5) = -2q + 9
Identity
a – 4a = 2a + 1 – 5a
No solutions
Homework - Practice 2-4 #7-38
Equations & Problem Solving
Practice 2-4
Equations & Problem Solving
Reteaching 2-3
Equations & Problem Solving
Solving Equations with Fractions
1. 42
2. 24
7. 5 1/9
3. 90 4. 30
8. 11 1/9
9. -3/4
6. 78
10. -14 2/7
12. 3/4n – 5 = 2n; -4
11. 1/2a + 8 = 24; 32 yrs
13. 0
5. 8 ¼
14. 2
Solving Equations with Decimals
1. 100 or 102 2. 1000 or 103
4. 0.3
5. 2.2 6. 4
9. 47.775
3. 10000 or 104
7. -5.8
8. 179
10. n – 0.08n = 1.38; 1.5
11. n + 0.35n = 0.675; 0.5
Equations & Problem Solving
Notes
Equations & Problem Solving
Notes
Homework – Practice 2-5 even
Formulas
Practice 2-5
Formulas
Notes
Literal equation – an equation involving two or more variables.
Examples – d = rt, P = 2w + 2l…
Transforming Geometric Formulas
Solve the formula for the area of a triangle for h.
A = ½ bh
Solve P = 2w + 2l for w…
Solve volume of a cylinder for h…
V = π r2h
Transforming Equations
y + 2x = 5 (solve for y)
Formulas & Measures of Central Tendency
Notes
y – 4 = 5x + 7 solve for x
Transforming Equations Containing Only Variables
m – hp = d (solve for p)
y–b=x
m
(solve for y)
(solve for m)
Lesson 2-7 Using Measures of Central Tendency
Mean, Median, Mode, Range, Stem & Leaf Plot
Solving an Equation
99, 86, 76, 95, x; mean 91
3.8, 4.2, 5.3, x; mean 4.8
Homework Practice 2-6 & 2-7 every 3rd problem
Using Measures of Central Tendency
Practice 2-6
Using Measures of Central Tendency
Practice 2-6 continued
Using Measures of Central Tendency
Practice 2-7
Using Measures of Central Tendency
Practice 2-7
~ Chapter 2 ~
Chapter Review
~ Chapter 2 ~
Chapter Review
~ Chapter 2 ~
Chapter Review
~ Chapter 2 ~
Chapter Review