Basic Concepts and Rules

Basic Concepts
1. An equation is a statement which contains two expressions that are equal.
E.g. 3x - 2 = 5 is an equation.

2. When we solve equations, we find the value of the unknown or variable in the equation. 
E.g. x = 8 is the solution to the equation x - 3 = 5.

3. Equations with the same solution are called equivalent equations. 
E.g. 2x + 3 = 11 and 3x = 12 are equivalent equations as x = 4 is the solution to both equations. 

4. A linear equation is an equation in which the highest power of the variable/unknown is 1.
E.g. 3x + 5 = 9 is a linear equation as the highest power of the variable, x, is 1.

Rules when solving linear equations
1. To solve an equation, we need to find the value of the unknown/variable.
2. The solution or root of an equation is the value of the unknown that will make the equation true. 
3. When you add, subtract, multiply or divide the same algebraic expression to or from each side of the equation, the resulting equation is equivalent to the original equation. 
E.g. if a = b, then
    a + c = b + c
     a - c = b - c 
     a x c = b x c
     a ÷ c = b ÷ c
4. If an equation contains brackets, remove all brackets by applying the distributive law of multiplication over addition or subtraction. 
E.g. a(x + b) = ax + ab
5. A fractional equation has an unknown in the denominator of a term. To solve a fractional equation, we need to transform it into a linear equation. Watch the following video on how this is done: 

Solving Algebraic Equations

We can represent real-life situations by using linear equations. By solving these linear equations, we can find the solutions to real-life problems. In other words, to solve word problems, we translate them to linear equations and then solve the resulting equations.  The solution or root of an equation is the value of the unknown that will make the equation true. 

Steps for solving problems:
1. Read and identify the unknown quantity.
2. Represent the unknown quantity by a letter, e.g. x.
3. Write expressions for other quantities in terms of x. 
4. Form an equation using the information given.
5. Solve the equation.
6. Write down the answer to the problem. 

Note!
- Always check whether the solution obtained satisfies the original problem. For example, if the problem requires a positive integer, remember to reject the negative integers in your answer. 
- Remember to only set one unknown and express the other unknown quantities in terms of x. If not, there will be too many unknowns in the equation to be solved.