Carl+P.,+Erece+F.,+Kadille+N.

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toc =[|Algebra]=

[|Animoto]
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[|Pre-Quiz]
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Solving for x
Solving for the value of the given variable

Equality
x = 3

= this sign means the equality of 2 sides

example: 3 = 3


 * [|variable]-** is a number that is represented using letters.

so if x = 3

x would be 3 to check, 3 = 3

Variable times a number
3x = 9

//a number times a variable is shown as number beside the variable note: the number is shown first before the variable so it looks like this e.g. 3x//

A number with(times) a variable is called as **[|numerical coefficient.]** 3x is only one term

to solve this, we need to find the value of x by looking this format, x = (number) if we already found that format, it means we found the value of x

in this process, we need to REMOVE THE NUMBER MULTIPLIED TO THE VARIABLE which is 3. to do that //we need to divide 3x by 3//. but before that, we need to understand that 3x IS 3 TIMES X.

the main goal for now is to make 3 as 1 so we are going to show it as 3/3 times x. since the equal sign means equality for both two side, when we divide 3 to the left side, we need to divide 3 to the other side too. leaving the problem as x = 9/3. now x is by itself, but we still have the fraction/division to solve so that we can find the format/answer we needed, x = a number. 9/3 contains two numbers, but since this was an equation, we can solve it, to be one number, 9 divided by 3 is 3 (9/3 = 3).

now we got the x = a number

x = 3

but there is a problem, good problem. we need to check it by substituting the number x in the equation.

there are 3 or more steps needed

for this problem, we are going to to 3 only

checking:

3x = 9 3(3) = 9 9=9

now, we are done.

//the truth is i think this book will help you, like novels, there are sentences that can catch your attention. this book can be found in the public library, i think it is 4th floor. the book is called "Bob Miller's Algebra For The Clueless" i think. a green book. and it caught my attention as i read the sentence in front of the book and it says "thanks for bob miller, not only did i pass, but i got an A!"// but you dont have to especially mr. 100 and the cute refresher.

2-term solving
x + 23 = 33

these problem have 2 terms

x is a variable +23 is a constant

order of operation said that the constant must be removed first

so the equation will look like this:

x + (23-23) = 33-23 x + 0 = 10 x = 10

check:

x + 23 = 33 (10) + 23 = 33 33 = 33

this equation have x by itself. if x is multiplied with a number remove the constant by using the opposite integer of the constant (e.g. -3 **+3,** 23 **-23**) then do the instructions i gave you in the one-term solving.

x + (23 **-23**) = 33**-23 x = 10**

Answers


worksheet source: http://www.teach-nology.com/worksheets/math/algebra/

Words to Algebraic Form
preview: try to solve this first number one does not mean 5-x it means x-5 number 2 is 5(x + 2) i looks like x + 2 putting the x at the first place to show it organized and it looks easier third one is 5x. when multiplying a number and an unknown number, variable, put them together and the number goes first not like this x5.
 * 1) five less than a number
 * 2) a number multiplied to the sum of a number and two
 * 3) five times a number

Algebraic form to Words
This is the opposite form of the other way. five less than the the sum of eight decreased by five and a number is also equal to [(8-5)+5]-5

it is done by trying to translate it by reading it with sense.

Geometry
sample source: [|Kadille's Scribe Post]

**Geometric Problems**

1. The length of the triangle is 3 times the width. the perimeter is 96 cm. Find the width and length. The sides are cm, _cm. This is the diagram of the problem This is to be done in solving this problem

let x = w. align all sides and their labels. place the perimeter is equal to 96. add all the sides of the rectangle and place it beside the perimeter. then solve for x

this is the solution of x. x = 12. i substitute the sides' label beside it resulting 3x to be 3(12). then simplify it ( 3 (12) to 36) and place it above the given perimeter or total. add the simplified length of each side to check if the total will be the given perimeter. and to finish this problem, we must finish it by answering the simple question.

The sides are 36 cm, 12 cm. Note: this is very important. you will lose most of the marks if this is not done.

2. the length of a rectangle is 5m greater than the width. the perimeter is 150m. find the width and the length.

simple sentence: the sides are m, _m.

diagram:

align the sides with their labels beside them. include the perimeter under the line with its value 150 m far away beside it.

this is the solution of the problem.

then answer the simple sentence: the sides are 40m, and 35 m.

3. the first side of a triangle is 8 m shorter than the second side. the third side is 45 times as long as the first side. the perimeter is 2 m. find the length of each side.

the simple sentence is : the sides are ___m,__ _m, m.

diagram:

this must be done to solve this problem

the solution of this problem

finish this problem by completing the simple sentence:

the sides are 3m, 11m, 12m.

4. the third side is 30 m shorter than twice the length of each congruent side. the perimeter is 570. find the length of each side

the sides are ___m,__ __m,__ __m.__

diagram:



the steps are indicated to the previous problems.

finish this problem by completing the simple sentence:

the sides are 150m, 150m, 270m.

Standard
sample souce:

**NOTE:** //standard problems is also the same as replacing algebraic equations using words but in problem form.//    **1.** The second of two numbers is 4 times the first. Their sum is 50. Find the numbers. The numbers are   and. **(You can also write this at the end of the equation)**__ 4x would be on the right side of the + sign, because it is the second number. The first number is x. So, the equation would be like this:Let x = first #x + 4x = 50  5x = 50 (combined terms)  x  __ 10 The answer is **10, 40**   You must write the formula x + 4x 50 10 + 4(10) = 50 10 + 40 = 50  50 = 50  x 10 4x 40  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">   <span style="COLOR: rgb(51,51,51)">    <span style="COLOR: rgb(51,51,51)">**2.** The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers. <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">The numbers are ,,and. **(You can also write this at the end of the equation)** <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">Two other # would equal x because we don't know anything about them. let x = small # 1 and small # 2 <span style="COLOR: rgb(51,51,51)"> x + 12 + x + x = 84 3x + 12 = 84 (combined terms) -12 -123x = 72 <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">x= 24 <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">The answer is **36, 24, 24** <span style="COLOR: rgb(51,51,51)">  <span style="COLOR: rgb(51,51,51)"> **4.** The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers. The numbers are  ,and. **(You can also write this at the end of the equation)** let x = first# <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">5 more than twice the first <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">2x + 5  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">the sum is 80  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">= 80  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">x + 2x + 5 = 80  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">3x + 5 = 80  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">- 5 -53  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">x 75 <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">3x 25 <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">2x+5 = 55 <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">x 25 <span style="COLOR: rgb(51,51,51)">The answer is **25, 55**   <span style="COLOR: rgb(51,51,51); FONT-FAMILY: Arial">   <span style="COLOR: rgb(51,51,51)">    <span style="COLOR: rgb(51,51,51)">**6.** Find two numbers whose sum is 92, if the first is 4 more than 7 times the second. Find the //first// number. <span style="COLOR: rgb(51,51,51)">The numbers are ,and. <span style="COLOR: rgb(51,51,51)">**(You can also write this at the end of the equation)**  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">let x  second # <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">(7x + 4) + x = 92   <span style="COLOR: rgb(51,51,51)"> 8x + 4 = 92 (combined terms)    <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">- 4 -4  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">8x = 88  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">8x = 11  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">(7x + 4) + x = 92  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">8(11) + 4 = 92  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">88 + 4 = 92  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">92 = 92x  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">= 117  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">x + 4 = 81  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: Arial">The answer is **11, 92**  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: Arial">  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: Arial">  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: Arial">**8.** Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as much as the bracelet. <span style="COLOR: rgb(51,51,51); FONT-FAMILY: Arial">The price is__. **(You can also write this at the end of the equation)** <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">Let x = bracelet  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">3x = Necklace  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">3x + x = 19  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">24x = 192  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">4x = $48 ($48.00)  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">3x = 3  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">(48)= 144  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">x = 48  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">$144.00+$48.00  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">$192.00  <span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">The price of a bracelet is **$48.00** and the necklace is **$144.00.**

Word Problems
source: http://www.teach-nology.com/worksheets/math/algebra/

<span style="COLOR: rgb(51,51,51); FONT-FAMILY: arial">***Quadratic Equation derived Video**
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Parent Information
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Game
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