# MandysNotes

## Step-By-Step How To Solve A Linear Equation Example One

21 March 2010
 4x - 2x - 5 = 4 + 6x + 3 Goal is to isolate x on one side to be able to solve. 2x - 5 = 7 + 6x Combine like terms. 2x - 5 + 5 = 7 + 6x + 5 Add 5 to each side. 2x = 12 + 6x Subtract 6x from each side. -4x = 12 Then, divide both sides by -4 x = -3 CHECK your solution by plugging back into the original equation.

Disclaimer: I did not create nor do I own these videos. I have simply embedded them, courtesy of YouTube.  (But I do think this teacher does a fantastic job with his video tutorial series.)

## Step-By-Step How To Solve A Linear Equation Using The Distributive Property

21 March 2010
 2(k - 5) + 3k = k + 6 Use the distributive property to simplify and combine like terms. 2k - 10 + 3k = k + 6 Combine like terms. 5k - 10 = k + 6 Then, add 10 to both sides. 5k = 16 + k Then, subtract k from both sides. 4k = 16 Then, divide both sides by 4 k = 4 CHECK your solution by plugging back into the original equation.

Disclaimer: I did not create nor do I own these videos. I have simply embedded them, courtesy of YouTube.  (But I do think this teacher does a fantastic job with his video tutorial series.)

## Sets of Numbers Examples Sets: Natural Numbers, Whole numbers, Integers

20 March 2010

Counting Numbers:

### {1, 2, 3, 4, 5, 6, ...}

BY THE WAY, "..." notates continuation going up infinitely.

The set of Natural Numbers $$\mathbb{N}\ \$$ = {0, 1, 2 3, 4, 5, 6...}.

The set of Integers, $$\mathbb{Z}\ \$$   = {..., -3, -2, -1, 0, 1, 2, 3}.

The set of Rational numbers, $$\mathbb{Q}\ \$$  is the set of ratios of integers.

That is, every $$q \in \mathbb{Q}\$$

is of the form:

$$q = \frac{n}{m} \$$

With $$n, m \in \mathbb{Z}\$$ .

The set of Real Numbers $$\mathbb{R}\ \$$  is the set of limits of sequences of rational numbers.

## Sets of Numbers

20 March 2010

A set is a collection of "elements," or "members," and each set is entirely determined by its members. If $x$is a member of a set $U,$ we write $x \in U.$ In basic algebra, the elements of a set are usually numbers.

We can also designate a set by enclosing its members in  braces , {   }.