Algebra

Algebra is a form of mathematics that combines letter and numbers with arithmetic operations. These letters represent unknowns values and are called variables. They are called variables because they can be used to represent different numerical values. For example: a is a variable that represent an unknown number.

Properties of variable Variables have the same properties as regular digits (Integers, fractions, etc.) Let’s look at some: 1. Addition and subtraction: Examples: a + 1 = a + 1 Here, because a is an unknown, the a – 1 = a - 1 operation remains as is. a + a = 2a Here, you can imagine that there is a 1 in front of the variable and that it can be added onto another identical variable. 2a + 3a = 5a Same story

1. Addition and subtraction: Examples: a – a = 0 Again, we have two similar variable. 4a – 1a = 3a 4a – 7a = -3a 5a + 6b = 5a + 6b In this, case, there are two different 5a - 6b = 5a – 6b variables and hence, they cannot be added or subtracted.

2. Multiplication: Examples: 2 x a = 2a Since a is an unknown variable that represents a numerical digit, it can multiply the 2. a x b = ab So two variables that represent unknown 2a x b = 2ab digits can be multiplied as usual. 2a x 2b = 4ab In this case, the numerical digits multiply and it’s status quo for the variables. a x a = a1+1 = a2 As in multiplication with exponents, the exponents are added together.

2. Multiplication: Examples: 2ab x 3ab = 2 x 3 x a x a x b x b In this case, identical = 6 a1+1b1+1 variables multiply. = 6a2b2

2. Division: Examples: 2 ÷ a = 2 Again, Here, because a is an unknown, a the operation remains as is. 2a ÷ a = 2 x a1-1 Only the identical variables perform the = 2 x a0 operation. = 2 x 1 = 2 4a2b ÷ 2a = 4 ÷ 2 x a2 ÷ a x b = 2 x a2-1 x b = 2 x a x b = 2ab

3. Fractions: Examples: 2 x 3 a a = 2 x 3 a x a = 6 a1+1 a2

3. Fractions: Examples: a x 3 2 a = a x 3 2 x a = 3a 2a = 3 2

Algebraic Equations

Now, don’t let algebra bring you down, it’s very simple.

Things to know before we get started. Algebra involves the use of variables such as x or y or z or any other letter that can designate any number. Imagine that algebraic equations are scales. A scale can be tilted if you add, subtract, multiply or divide either side. So what you do on one side of the equation must be done on the other. Let’s look at the following example.

So: 2x + 2 = 8 My objective is to solve for x. To do so, I have to isolate x i.e. have x by itself on one side. We’ll start by subtracting the 2 being added because that will eliminate the 2. But remember that what you do one side you must do on the other. 2x + 2 -2 = 8 -2

So: 2x + 0 = 6 2x = 6 Now, I have to eliminate the other 2 that is multiplying the x. To do so, since it is multiplying the x, I will divided it by 2 because the opposite of multiplication is division. Again, what you do one side, you must do on the other. 2 2

So: 5. x = 3 Now, try solving the following equation by your self: 3x + 5 = 14