Simple equations

Simple Equations

However, when most people talk about equations, they mean algebraic equations. These are equations that involve letters as well as numbers. Letters are used to replace some of the numbers where a numerical expression would be too complicated, or where you want to generalize rather than use specific numbers.

Algebraic equations are solved by working out what numbers the letters represent. We can turn the two simple equations above into algebraic equations by substituting x for one of the numbers:

2 + 2 = x

We know that 2 + 2 = 4, which means that x must equal 4. The equation answer is therefore x = 4.

5 + 3 > 3 + x

We know that 5 + 3 = 8. The equation tells us that 8 is greater than (>) 3 + x.

Take 3 away from 8, to get 5.

We can see that x must be less than 5 or x is 4 or less. x < 5 or x <= 4

We cannot say more precisely what x is with the information that we are given.

There is no magic about using the letter x. You can use any letter you like, although x and y are commonly used to represent the unknown elements of equations.

Terms of an Equation

A term is a part of the equation that is separated from other parts by an addition or subtraction sign.

Terms may be just numbers, or they may be just letters, or they may be a combination of letters and numbers, such as 2x, 3xy or 4×2.

In a term involving letters and numbers, the number is known as the coefficient, and the letter as the variable.

Terms that have exactly the same variable are said to be like terms, and you can add, subtract, multiply or divide them as if they were simple numbers.

ASSESSMENT 

The equation 2x + 3x is equal to 5x, simply 2 lots of x plus 3 lots of x to make 5 lots of x (5x).

5xy –xy = 4xy

5y × 3y = 15y.

You cannot add or subtract unlike terms. However, you can multiply them by combining variables and multiplying the coefficients together.

So, for example, 3y × 2x = 6xy (because 6xy simply means 6 times x times y).

You can divide unlike terms by turning them into fractions and cancelling them down. Start with the numbers, then the letters.

So, for example, 6xy ÷ 3x =

6xy         =             2xy         =             2y           =             2y

3x                          x                             1