• EQUATIONS
  • SOLVING EQUATION
  • WORD PROBLEMS WITH EQUATIONS


EQUATION
An equationis a mathematical statement that has an expression on the left side of the equals sign (=) with the same value as the expression on the right side.

One of the terms in an equation may not be know and needs to be determined. Often this unknown term is represented by a letter such as "x".

Example: 5+x = -2
Solving an equation means manipulating the expression and finding the value of the unknown variables.You must isolate the variable

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Several symbols are used to relate all of the variables and constants together.
These symbols are listed and explained below.


*
Multiply
/
Divide
+
Add or Positive
-
Subtract or Negative
( )
Calculate what is inside of the parentheses first. (also called grouping symbols)

SOLVING EQUATIONS
When solving equations, remember that addition and subtraction are inverse operations
To solve equations using addition and subtraction, first decide which operation has been applied, then use the inverse operation to undo this (remember to add or subtract from both sides of the equation).

Example

Solve: x + 79 = 194
Solution: x + 79 = 194 x + 79 - 79

194 - 79 x

115

You need to get the variable by itself (isolate the variable).
To undo adding 79, subtract 79 from both sides.
Equations involving the use of multiplication and/or division.

When solving equations, remember that multiplication and division are inverse operations, therefore they undo each other (i.e., (4 * 8)/8 = 4). To solve equations using multiplication or division, first decide which operation has been applied, then use the inverse operation to undo this (remember to multiply or divide on both sides of the equation).


Solve: 6x = 36
Solution: 6x = 36 (6x) / 6

36 / 6 x=6


You need to get the variable by itself (isolate the variable).
To undo multiplying by 6, divide by 6 on both sides.


Complex equations that involve different combinations of multiplication, division, addition, and subtraction.

pfeil053.gifIMPORTANT THINGS TO REMEMBER



Order of operations:
  • The operations inside parentheses () and brackets [] are done first.
  • Then any operations involving exponents
  • Then do all multiplying and dividing from left to right.
  • Finally, do all addition and subtraction from left to right.



When solving complex equations, be sure to remember that multiplication and division are inverse operations along with addition and subtraction.

To solve these equations, first decide which operation has been applied and then use the inverse operation to undo this (remember to apply the operation to both sides of the equation).

EXAMPLE

Solve: 7x - 7 = 42
Solution: 7x - 7 = 42
7x - 7 + 7 =42 + 7
7x=49
(7x) / 7=49 / 7
x=7

The variable needs to be isolated.
To undo subtracting 7, add 7 to both sides.
Adding 7 hasn't isolated the variable, so we need to continue.
To undo multiplying by 7, divide both sides by 7.

And now be fun and play equations
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http://www.shodor.org/interactivate/activities/AlgebraQuiz/

http://www.mathsnet.net/algebra/equation.html

http://www.quia.com/rr/42586.html

Quadratic equations formula





Word problems as equations

When converting word problems to equations, certain "key" words tell you what kind of operations to use: addition, multiplication, subtraction, and division. The table below shows some common phrases and the operation to use.
Word
Operation
Example
As an equation
sum
addition
The sum of my age and 10 equals 27.
y + 10 = 27
difference
subtraction
The difference between my age and my younger sister's age, who is 11 years old, is 5 years.
y - 11 = 5
product
multiplication
The product of my age and 14 is 168.
y × 14 = 168
times
multiplication
Three times my age is 60.
3 × y = 60
less than
subtraction
Seven less than my age equals 32.
y - 7 = 32
total
addition
The total of my pocket change and 20 dollars is $22.43.
y + 20 = 22.43
more than
addition
Eleven more than my age equals 43.
11 + y = 43
Copy in your notebook and do the following word problems

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