MandysNotes

21 March 2010 In Properties of Real Numbers

For all real numbers A, B and for when C does NOT equal 0, the equations:

A = B and AC = BC are equivalent to one another.

Each side can be multiplied by the same NONZERO number without changing the solution set.

21 March 2010 In Properties of Real Numbers

For all real numbers A, B and C, the equations:

A = B and A + C = B + C are equivalent to one another.

The same number may be added to each side of an equation without altering the solution set.

21 March 2010 In Linear Equations

As the name suggests, a linear equation in one variable implies that there is only ONE variable, and that the equation involves only real numbers. A linear equation in one variable can be written in this form: Ax + B = C where A does NOT equal zero.

A linear equation is also a first-degree equation, since the greatest power of any variable is 1.

Here are some examples of linear equations in one variable:

x + 2 = -1

x - 3 = 5

3k + 4 = 10

21 March 2010 In Linear Equations

Equations and Expressions are closely related.

The primary difference between the two is an equals sign. An "equation" has a left side, a right side and an equals sign separating the sides. An "expression," by contrast, doesn't have any "sides" and is simply what the name suggests: An algebraic "expression." Though sometimes it is possible to combine like terms, we are generally not expected to "do" or "solve" anything regarding expressions.

For example:

3x - 7 = 2

This is an EQUATION, because it has a left side, a right side, and an = sign separating the two.

3x - 7

This is an EXPRESSION, because there are no "sides" and no = sign.

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