# Understanding Algebra by James Brennan

By James Brennan

Downloaded from http://www.jamesbrennan.org/algebra/

**Read or Download Understanding Algebra PDF**

**Similar instruction methods books**

This source provides complete assurance of the area warfare I interval. global battle I: fundamental resources provides 33 complete or excerpted basic resource fabrics, together with diaries, speeches, letters, journals and memoirs, which are with regards to the interval. different positive factors contain photographs and maps, a close chronology of occasions, sidebars that includes similar details, an index, a thesaurus of "Words to Know," learn and job principles, and a listing of additional analyzing assets.

**Western Civilization: Beyond Boundaries, Vol. 1: To 1715**

Western Civilization, 5/e, is wonderful for its wider definition of Europe that incorporates japanese Europe, Scandinavia, and eu frontiers. spotting that components outdoor the continent affected eu historical past, the authors spotlight Europe's position on the planet in the course of the narrative and within the basic resource function, "The international checklist.

**Physics for Scientists and Engineers (with PhysicsNOW and InfoTrac )**

The booklet used to be in incredible situation. nice expense for a slightly dear publication. fast transport too.

Robert Stalnaker explores the proposal of the context during which speech happens, its position within the interpretation of what's stated, and within the clarification of the dynamics of discourse. He distinguishes diverse notions of context, however the major concentration is at the inspiration of context as universal flooring, the place the typical floor is an evolving physique of history details that's presumed to be shared through the contributors in a talk.

- Western Civilization in World History
- Student Teaching: A Journey in Narratives
- Aquinas’ Proofs for God’s Existence: St. Thomas Aquinas on: “The Per Accidens Necessarily Implies the Per Se”
- The Murder of History: A Critique of History Textbooks Used in Pakistan

**Extra info for Understanding Algebra**

**Example text**

This is, of course, a ridiculously simple example, but it makes the point. Equations that have this property are called identities. Some examples of identities would be 2x = x + x 3=3 (x – 2)(x + 2) = x2 – 4 All of these equations are true for any value of x. The second example, 3 = 3, is interesting because it does not even contain an x, so obviously its truthfulness cannot depend on the value of x! When you are attempting to solve an equation algebraically and you end up with an obvious identity (like 3 = 3), then you know that the original equation must also be an identity, and therefore it has an infinite number of solutions.

Infinite Number of Solutions Consider the equation x=x 45 Chapter 2: Introduction to Algebra This equation is obviously true for every possible value of x. This is, of course, a ridiculously simple example, but it makes the point. Equations that have this property are called identities. Some examples of identities would be 2x = x + x 3=3 (x – 2)(x + 2) = x2 – 4 All of these equations are true for any value of x. The second example, 3 = 3, is interesting because it does not even contain an x, so obviously its truthfulness cannot depend on the value of x!

46 Chapter 2: Introduction to Algebra What we want to do when we solve an equation is to produce an equivalent equation that tells us the solution directly. Going back to our previous example, 2x + 3 = 7, we can say that the equation x=2 is an equivalent equation, because they both have the same solution, namely x = 2. We need to have some way to convert an equation like 2x + 3 = 7 into an equivalent equation like x = 2 that tells us the solution. We solve equations by using methods that rearrange the equation in a manner that does not change the solution set, with a goal of getting the variable by itself on one side of the equal sign.