Algebra generally occurs in the form of:

• words
• or already expressed calculations.

In algebra the letters that you see are just representatives of an unknown number. They're called variables and you can also substitute in numbers there.

Algebra's kind of like a recipe, it shows you the steps but sometimes not the ingredients.

There are ways that algebra is expressed in its most simplest form (for ease). This is called simplification.

Here are some general rules:

• Addition – same variable, just add together. E.g. 2x + 5x + 2, x^2 + 4x + x
• Subtraction – same variable, just subtract. E.g. 5x – 2x + 1
• Multiplication – combine together. E.g 5 x x x 6x x 2y
• Division – see video.2x / 4x, 2x/5x. 2x/5y

You can even substitute in numbers (ingredients) to see if the formula/expression works (recipe).

• g. 2x + 5x + 2, x^2 + 4x + x

Working with equations

The key to solving equations is isolate out the variable. It pretty much involves using the opposite sign and moving things to the other side. Let me demonstrate with the following examples.

• 2o + 4 = 20
• o + 20 = 50
• o – 20 = 5
• 4x/10 = 4/5

Working with inequalities

Similar process as working with equations however:

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality must change.
The solution of an inequality will be a range of values for the variable, rather than just one value.

• 2o + 4 < 20
• o + 20 > 50
• o – 20 < 5
• 4x/10 > 4/5

Now, let's go through some example questions:

Q19 - Which inequation shows the following statement? x is greater than 7 but less than or equal to 10

A 10 > x > 7 B 10 < x < 7 C 10 < x > 7 D 10 < x > 7 E 10 < x > 7

Q29 - If V= [(x-y)/4] then x equals

A Y + 4V B Y - V C Y/4 + V D Y + V/4 E 4(Y + V)

Q30 - Solve the inequation for y

9(y + [2/3]) < 7

A Y > -1/9 B Y < -1/9 C Y > 1/9 D Y< 1/9 E None of these

EXTENSION: EXPANSION, FACTORISING AND SURDS

Expansion

Expanding brackets involves removing the brackets from an expression by multiplying out the brackets. This is achieved by multiplying every term inside the bracket by the term outside the bracket.

Let's expand:

• 3(x+6)
• 6(4a−10).

Factorisation

Factorisation is the opposite process of expanding brackets. For example, expanding brackets would require 2(x+1) to be written as 2x+2. Factorisation would be to start with 2x+2 and to end up with 2(x+1).

Let's factorise:

• 2x+2
• 2x^2 + x - 3

To factorise:

• Take out common factors.
• Put the equation back together.

Surds

When we can't simplify a number to remove a square root (or cube root etc) then it is a surd!

Example: √2(square root of 2) can't be simplified further so it is a surd

Example: √4(square root of 4) can be simplified to 2, so it is not a surd!

Have a look at some more examples of simplifying surds:

• √2 x √4
• √100 x √4
• √2 + √4

Surds have a decimal which go on forever without repeating - they are actually Irrational Numbers.

Now, let's do some extension questions.

Q23 - Simplify 5√124 completely

A 10√31 B 7√31 C 20√31 D 10√62 E None of these

Q20 - Expand and simplify

7(x+2) + 5 =

A 7x + 19 B 7x - 19 C 7x - 9 D -7x + 19 E None of these

Q37 – [15y/2] x [x/5]

A 3xy/2 B 15x/10y C 3x/2y D 3xy E None of these

Q48 - If x = 1/6 and y = 2/9. Evaluate (2x + 3y)(2x – 3y)

A 1/2 B 2/3 C 1/3 D -1/3 E None of these

Q 49 Expand and simplify (a + 6)(a – 6)

A a^2 - 36 B a^2 + 6a - 36 C a^2 - 6a -36 D a^2 + 36 E None of these

Q50 - Factorize and simplify a^2 – 6a + 9

A (a – 3)(a – 3) B (a + 3)(a – 3) C (a + 3)(a + 3) D (a – 3)(a + 3) E None of these

Let's now do a full recap!

Now it's time to do your assignment.

1. Download the assignment question here.
2. Print it out or if you want to do it electronically, save it.
3. Complete the questions to it.
4. Then check the solutions on the video below or download the ANSWER KEY here.