• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2

# Algebra Basics

Extracts from this document...

Introduction

Algebra is quite an interesting topic, which many people struggle on,

However I will explain the basics of it, the basics is that everything should be balanced in every equation question

for example if there is a question of 2x+8=12x, you would need to make the xs balance in one side, whilst the number (being 8, here) is with its kind of numbers, so now the equation reads 8=12x-2x, as the 2x moves over it becomes from positive to negative, so it is 12x-2x which gives 10x, so now the equation is 8=10x

So now 10 divide by 8= 10/8=5/4 as a fraction.

Another example is 6+3x=12x-4

Balance the equation so its 6+4=12x-3x, which is 10=9x

9 divided by 10=9/10, and leave it as that.

Middle

Subtract 23 from each side         x + 23 - 23         =         45 - 23

Result / Answer         x         =         22

The diagram below shows a more complex equation. This equation has both a constant and a variable on each side. Again, to solve this you must keep both sides of the equation equal; perform the same operation on each side to get the variable "x" alone. The steps to solving the equation are shown below.

Initial Equation / Problem:         x + 23         =         2x + 45

Subtract x from each side         x - x + 23         =         2x - x + 45

Result         23         =         x + 45

Subtract 45 from each side         23 - 45         =         x + 45 - 45

Result         -22         =         x

Take a look at the equation below. As you

Conclusion

Recall beginning to solve the equation "x + 23 = 3x + 45". Applying addition and subtraction gave

2x         =         -22

But our end goal is to determine what x is, not what 2x is! Imagine that three investors own an equal share in the company Example.Com. The total worth of Example.com is \$300,000. To determine what the share of each investor is, simply divide the total investment by 3:

\$300,000 / 3 = \$100,000

Thus, each investor has a \$100,000 stake in Example.com. We apply the same idea to finding the value of x. However, instead of dividing by the number of investors, we divide by the coefficient of the variable. Since we determined that the coefficient of x is 2, we divide each side of the equation by 2:

After dividing by 2         1x         =         -11

Finally rewritten as         x         =         -11

• = Subtraction

/ = Divide

* = Multiplication

This student written piece of work is one of many that can be found in our GCSE Consecutive Numbers section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Consecutive Numbers essays

1. ## GCSE Maths Coursework - Maxi Product

I will see in decimal numbers if I can retieve a higher result than 125 when three numbers are multiplied together. (5.1,4.8,5.1)= 15 --> 5.1+4.8+5.1 --> 5.1x4.8x5.1=124.848 (5.3,4.4,5.3)= 15 --> 5.3+4.4+5.3 --> 5.3x4.4x5.3=123.596 I will now move on to fractional numbers as there is no decimal number that can give a result higher than 125 using three numbers.

2. ## Investigate the Maxi Product of numbers

Number Two numbers used Two numbers added Two numbers multiplied Maxi Product 14 1 and 13 1+13 1x13 13 14 2 and 12 2+12 2x12 24 14 3 and 11 3+11 3x11 33 14 4 and 10 4+10 4x10 40 14 5 and 9 5+9 5x9 45 14 6 and

1. ## Investigate calendars, and look for any patterns.

20 numbers 1 2 3 4 5 1 x 26 = 26 8 9 10 11 12 5 x 22 = 110 15 16 17 18 19 Difference = 84 22 23 24 25 26 I decided to plot a table summarising the above results: Ex.

2. ## In this investigation I will explore the relationship between a series of straight, non-parallel, ...

Cross-Over Points Open Regions Closed Regions Total Regions 1 0 2 0 2 2 1 4 0 4 3 3 6 1 7 4 6 8 3 11 5 10 10 6 16 6 15 12 10 22 Open Regions

1. ## I am to conduct an investigation involving a number grid.

32 33 34 41 42 43 44 51 52 53 54 [image047.gif] 31 x 54 = 1674 51 x 34 = 1734 1734 - 1674 = 60 The difference between the two numbers is 60 Box 3 63 64 65 66 73 74 75 76 83 84 85 86 [image048.gif]

2. ## Study the topic of trios and work on from that, to discover patterns and ...

For example, factorial 4 is the number 4 multiplied by every integer down to one inclusive. I.e. Factorial 4 is: 1 x 2 x 3 x 4 = 24 and factorial 5 is: 1 x 2 x 3 x 4 x 5 = 120.

1. ## About Triangular Square Numbers

it is beginning to look like 1.4142... = . Now one can apply the first rule: to find p(N7), Now one can apply the second rule to see if it yields the same result: Voila! The same result. Since the index, 7, is odd, it follows that t(N7)

2. ## Investigation to Find the number of diagonal of any 2 Dimensional or / and ...

� n + something For the sequence above, the rule 3�n + something would give the values 3�1 + something = 3 + something 3�2 + something = 6 + something 3�3 + something = 9 + something 3�4 + something = 12 + something 3�5 + something = 15

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to