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Appetizers and Lessons for Mathematics and Reason
  online logic chapters  - the best starting point for further site exploration.  Bon Appetite.

C. Solving Linear Eq'ns - No Sticks
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Solving Linear
Equations
(Feb 14, 2005)
with & then without stick diagrams plus   solving word problems; and solving systems: -  essentially one unknown, essentially triangular & general

 

A. Letters and Lengths
B. Solving Linear Eq'ns - WS
C. Solving Linear Eq'ns - No Sticks
D. Almost One
E Substitution Methods
F. Two More Methods
G. Larger Systems
H.  Exercises to Try

Solve 4x + 10 =  30
Solve 3x -4 = -11
(¼)x = x - 9
Solve ax+b = cx + d

Read them in order

(i) x + 20 = 29 WS
(ii) 2x + 6 = 24 WS
(iii) 3x + 10 = 32 WS
(iv) 5a + 16 = 3a+ 24 WS
(v)  (½)x + 8 = 24½ WS
(vi)  (¾)a + 16 = (¼)a+ 24 WS
(vii) (¾)q + 17 = 32 WS
(viii) 13 =[2/3]x +7 twice WS
(5/6)q + 8+(5/6) = 14 + (2/3) WS
Proper Use of Equal Sign

Up
A. Letters and Lengths
B. Solving Linear Eq'ns - WS
C. Solving Linear Eq'ns - No Sticks
D. Almost One
E Substitution Methods
F. Two More Methods
G. Larger Systems
H.  Exercises to Try
 


Solving Linear Equation 
(without stick diagrams)

Here are several examples in which we solve equations  without the use of stick diagrams.   Here are more examples. 

Solve 4x + 10 =  30
Solve 3x -4 = -11
(¼)x = x - 9
Solve ax+b = cx + d

Explore them one at a time, one after another. Bon Appetite.

 

 

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Math How-TOs
1. Arithmetic   2. Algebra   3.  More Algebra  4.  Geometry 5 More Geometry 6.  Calculus
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Online Volumes (orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&.More.Math.1995

Skill & Concept 
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 1. Decimal Arith - Video Based ]
2   Fractions  
3.  Fractions  with Units  
3. Solving Linear Equations  - 
making alg easier
4. Formulas forwards & Backwards - unifying theme for Algebra
5.  Proportionality, Back- & For-wards - theme at work.
6.  Logic - Math Free, good for precision in  work & studies 
7. Euclidean-Geometry  (leanly)
8. Slopes and Lines 
9. Why Study Slopes - a context 
10.  Quadratics
11  Polynomials
12  Factored Polys - a context
13 Functions - For-& Back -wards
14  Number Theory, Richly
15. Exponents, Radicals & logs.  
16   Calculus - Examples & Advice 
17.   Real  Analysis 
18  Electric Circuits Etc (So So)
19 Maps, Similarity & Trig, (alt view)
20 Complex numbers  
21 Logic with Symbols+truth tables
22  Consistent Story Telling
23. Even More Logic

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