Transforming+Equations

=  Transforming Equations wiki space created by: Matthew Joyce with Mr.Morgans Algebra II class. Last update on: 12/15/08 Hope my page is helpful.   =

Solving Equations and Problems //** 3-1 Transforming Equations: Addition and Subtraction **//
 * Notes on the Subject **: The following includes all notes on the subject matter and examples of the transforming equations

Addition Property of Equality
If a, b and c are any real numbers, and a = b, then a + c = b + c and c + a = c + b If the same number is added to equal numbers, the sums are equal.

Subtraction Property of Equality
If a, b and c are any real numbers, and a = b, then a - c = b – c. If the same number is subtracted from equal numbers, then the differences are equal. Equations having the same solution over a given domain are called **equivalent equations** over that domain.

Transforming an Equation into an Equivalent Equation
Equation //** 3-2 Transforming Equations: Multiplication and Division **//
 * //Substitution//** Substitute an equivalent expression for any expression in a given
 * //Addition//** Add the same real number to each side of a given equation
 * //Subtraction//** Subtract the same real number from each side of a given equation.

Multiplication Property of Equality
If a, b and c are any real numbers, and a = b, then ac = bc and ca = cb If equal numbers are multiplied by the same number, then the products are equal.

Division Property of Equality
If a, and b are any real numbers and c is nonzero, and a = b, then a ¸ c = b ¸ c If equal numbers are divided by the same //nonzero// number, the quotients are equal.

Transforming an Equation into an Equivalent Equation
number Number //** 3-3 Using Several Transformations **// Since solving an equation “undoes” the building of it, we must work the order of operations in reverse order. Therefore we must start with addition and subtraction, and then do multiplication and division. Because they “undo” each other, addition and subtraction are called **inverse operations**, as are multiplication and division. For all real numbers a and b, (a + b) – b = a and (a – b) + b = a For all real numbers a and all nonzero real numbers b, (ab) ¸ b = a and (a ¸ b) b = a //** 3-4 Using Equations to Solve Problems **// Recall:
 * //Multiplication//** Multiply each side of a given equation by the same nonzero real
 * //Division//** Divide each side of a given equation by the same nonzero real

Plan for solving Word Problems
1. Read the problem carefully! Decide what unknowns are asked for and what facts are given 2. Choose a variable and use it with the given facts to represent the unknowns described in the problem. 3. Reread the problem and write an equation that represents relationships among the numbers in the problem 4. Solve the equation and find the unknowns asked for. 5. Check your results with the words of the problem. Answer the question. //** 3-5 Equations with the Variable on Both Sides **// Just as with non-variable terms, you can add/subtract, multiply or divide terms with variables. Get the variable onto one side of the equation and solve from there just as before. Sometimes when solving an equation, you end up with one number equaling another number, and you have no variable. If this is the case, as in 3 = 7, we say the equation has **NO SOLUTION**, or that the solution is the **EMPTY SET**. Other times, you may end up with a number equaling itself, such as in 4 = 4. If this is the case, we say that the solution to the equation is **ALL REAL NUMBERS**

** Examples: ** Here is an easier example of transforming equations: -5= n + 13 subtract 13 -5 - 13 = n + 13 - 13 -18 = n

Here is a harder example of transforming equations: Follow the example as it goes through each step. 2y - 5(y-3) = 7 - y 2y - 5y + 15 = 7 - y -3y + 15 = 7 - y -3y + 15 + y = 7 - y + y -2y + 15 = 7 -2y + 15 - 15 = 7 - 15 -2y = -8 -2y divided by -2 = -8 divided by - 2 y = 4 **Media File:** Powerpoint presentation on transforming equations:[|power point on transforming equations]

Here are two youtube video links too for your help.. I could not directly import them due to the school firewall. [|www.youtube.com/watch?v=gCyWqZx4ZbI], [|www.youtube.com/watch?v=biyKxig2dz4]

**Hyperlinks: My suggestion to you is to check out more of the notes, powerpoint, and the youtube videos more so than the the hyperlinks as the others were more helpful in me understanding the subject. However, the second link is extremely helpful so check it out.** The following websites will provide additional information on the subject of Transforming Equations:[|Transforming Equations online book] ( Transforming Equations is on page 73 of the previous link ) . The following is a very helpful link that is a visual and an audio guide on transforming equations [|interactive help on transforming equations].

1.) 6u + 3 = - 45
 * Quiz Questions :**

2.) 8 - (1 + 3p) = -8

3.) 7y - 2(y - 13) = 26

4) c -3(c - 17) = 11

5.) 3/5r = 42

SEE ANSWERS AT BOTTOM OF PAGE.

1.- Moyer, Robert. "College Algebra." __College algebra:third addition__. 14 Nov. 2008 http://books.google.com/books?id=i4ic0GqQh9QC&pg=PA73&lpg=PA73&dq=transforming+equations&source=bl&ots=81oiawpXIi&sig=BdgR86apKpKds6Lb4nmMRAF4hTk&hl=en&sa=X&oi=book_result&resnum=1&ct=result#PPA72,M1 2.- Colbert. "Mrs. Colbert's Algebra Readiness Class." __Mrs. Colbert's Algebra Readiness Class__. 14 Nov. 2008 <http://ww4.fsusd.k12.ca.us/schools/grange/teachweb/carlaco/powerpoints.htm>.
 * Citations :**

3.-"(uknown)." __HStutorials.net__. 15 Nov. 2008 <http://www.hstutorials.net/math/alg1_dolciani/a1d_03.htm>.

-Schamber. "Miss Schamber's Web Assistant." __Miss Schamber's Web Assistant__. <http://ws017.k12.sd.us/default.htm>.

ANSWERS TO QUIZ QUESTIONS: 1. -8 2. 5 3. 0 4. 20 5. 70