MandysNotes

21 March 2010 In Linear Equations

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.)

21 March 2010 In Linear Equations

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.)

20 March 2010 In Basics & Number Properties

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.

 

20 March 2010 In Basics & Number Properties

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 , {   }.

NOTRad