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EQUATIONS and Expressions:

EQUATIONS: Translating WORDs into the Language of Math.
Solving Problems using Logic, Diagrams and Math

VIDEOS

4.1 Virtual Nerd: Converting Words into Expressions
4.1 Virtual Nerd: Solving an Expression
4.2 Equivalent Expressions
4.2 What is a Rational Number
4.2 Checking for Equivalent Expressions
4.3 Using the Associative Porperty: Like Lerms
4.3 Simplest Terms
4.4 Distributive Property
4.4 Identity Equation

TOPIC-4 TEST:




An EXPRESSION is a mathematical 'sentence' comprised of

Numbers, Operations, and Variables.

You cannot solve an Expression: only Combine Like Terms and Simplify:

3a + 6 + 2a + 4b + 7a + 5 + b

3a + 2a + 7a + 4b + b + 6 + 5

12a + 5b +11


An EQUATION contains an EQUAL (=) Sign

D-C-M-A-M
Don't call me A Marshmallow
Don't call me After Midnight
Distribute, Combine, Move (BY: Add or Subtract) (Multiply or Divide)

WHATEVER YOU DO TO ONE SIDE, YYOU MUST DO TO THE OTHER

BALANCE THE EQUATION!

Examples:
1-STEP Equations:
4 + V = 7 --> so move the '4' by subtraction: V = 7 - 4 or 3
V - 10 = 15 --> so move the 10 by addition: v = 15 + 10 or V =25
3v = 21 --> so move the '3' by division : V = 21/3 or 7
v/5 =30 -> so move the '5' by multiplication : v = 30 * 5 or V = 150

If the coefficient of a variable is a fraction, Multiply by the Reciprocal:
(3/5)V = 21 so V = 21 x(5/3) or V = 7 x 5 = 35

2-Step Equations:
4v + 3 = 23: Step 1: Move by Subtraction: 4v = 23 -3 so 4v = 20. Then Step 2: Solve by division: V = 20 / 4, so V = 5.
6v - 2 = 16: Step 1: Move by Addition: 6v = 16 + 2 so 6v = 18. Then Step 2: Solve by division: V = 18 / 6, so V = 3.

COMBINE:
6 + 4v + 2 = 2v + 4 + 6v Combine Like Terms
4v + 8 = 8v + 4 Move Numbers to one side, Variable to the other. (subtract '4' from both sides)
4v + 8 - 4 = 8v + 4 - 4 --> 4v + 4 = 8V Move the '4v' by subtraction:
4v - 4v + 4 = 8v - 4v Combine --> 4 = v4 Move by Division
v = 4/4 = 1

Combine Like Terms SOLVER

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WORKSHEET LINKS

B07_Guess and Go
B-76 Substitution of Variables
E-70 Substitution
E-71 One Step Addition
E-72 One Step Addition
E-73 One Step Multiplication
E-74 One Step Multiplication
E-75 One Step Mixed Operations
E-76 Two Step
E-77 Equations

More Practice Problems