Noun

equations

  1. Plural form of equation.
Category: English plurals

From Wiktionary under the GNU Free Documentation License.
Fri Jul 10 09:08:12 2009

An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in

The equations above are examples of an equality: a proposition which states that two constants are equal. Equalities may be true or false.

Equations are often used to state the equality of two expressions containing one or more variables. In the reals we can say, for example, that for any given value of x it is true that

The equation above is an example of an identity, that is, an equation that is true regardless of the values of any variables that appear in it. The following equation is not an identity:

It is false for an infinite number of values of x, and true for only two, the roots or solutions of the equation, x = 0 and x = 1. Therefore, if the equation is known to be true, it carries information about the value of x. To solve an equation means to find its solutions.

Many authors reserve the term equation for an equality which is not an identity. The distinction between the two concepts can be subtle; for example,

is an identity, while

is an equation, whose roots are x = 0 and x = 1. Whether a statement is meant to be an identity or an equation, carrying information about its variables can usually be determined from its context; or by making a distinction between the equality sign ( = ) for a statement not true except perhaps in particular situations, and the equivalence symbol () for statements know to be true without further specification.

Letters from the beginning of the alphabet like a, b, c... often denote constants in the context of the discussion at hand, while letters from end of the alphabet, like x, y, z..., are usually reserved for the variables, a convention initiated by Descartes.

From Wikipedia under the GNU Free Documentation License
Thu Nov 5 06:38:07 2009

What is the easiets way to balance equations?
Q. It may be simple for so many other people, but it is so hard for me. I find many other things in Chemistry like mole ratios and other stuff to be a breeze but balancing equations really mess with me. Any suggestions on how to balance equations in a simpler way?
Asked by TinCan - Sun Feb 25 21:59:58 2007 - - 3 Answers - 0 Comments

A. The typical way I balance equations is to first divide the equation into reactants and products. (I usually do this by drawing a vertical line to separate both sides of the equation.) Then I write out every element, usually under the specific molecule. For each element, I write how many (i.e., if my molecule has 2 nitrogen I would write N = 2). One other tip is to include total elements, if more than one molecule has the same element (on one side of the equation). For this, I just total up all of that specific element and then write it in - usually towards the bottom of the page. Once I have all of my elements listed, with their corresponding numbers, I just start from the left side of the equation and check how many of that element… [cont.]
Answered by Cooper - Sun Feb 25 22:10:46 2007

How is the goal of solving equations with the variable on each side the same as solving multi-step equations?
Q. How is the goal of solving equations with the variable on each side the same as solving multi-step equations? Describe the steps to solve the equation 4x + 8 = 2x 6.
Asked by Daisy Anderson - Tue Jun 9 02:07:31 2009 - - 1 Answers - 0 Comments

A. 4x-2x = -6-8 2x = -14 x = -7
Answered by jess4lyfe - Tue Jun 9 02:18:14 2009

How do I solve complex systems of equations with linear combinations?
Q. Apologies; Over the years I have forgotten. When I ask "complex", I mean that you can't just multiply/divide 1 side to reach an equation that is simple to add/subtract to solve. The system of equations I am currently attemping to solve is as follows: 3x - 4y = 21 4x + 2y = 6 I know how to solve this equation using substition and graphing but am unable to do it with linear combinations. Thanks! Any assistance is greatly appreciated!
Asked by Neil - Thu Aug 17 15:18:57 2006 - - 10 Answers - 1 Comments

A. Any linear equations that can be put into the form a0x+b0y+c0z+...p0q=k0 a1x+b1y+c1z+...p1q=k1 a2x+b2y+c2z+...p2q=k2 * * anx+bnx+cnz+...pnq=kn are called simultaneous' equations if they have (or we think that they may have) a common solution point. Equations in this form can *always* be 'reduced' to the form (called 'upper triangular') 0x+ss0y+ 0x+... 0p=ue0 0+ ss1y+ 1x+... 1p=ue0 0+ 0+ 3x+... 3p=ue0 * * 0+ 0+ 0+... np=uen by adding and/or subtracting multiples of various rows to other rows. When complete p=uen/ n and the rest of the variables may be found by continued back substitution. This is called the 'Gauss-Jordan Elimination' method. If there is a problem and the family of equations 8cannot8 be put in upper… [cont.]
Answered by doug_donaghue - Thu Aug 17 16:32:42 2006

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Does this program have science . equations. or formulas you can insert? If not, how would you insert any unique symbols?

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