1. Maths Unit 7 (F) – Equations & Sequences
Solving equations with unknowns on both sides
Decide which side of the equation has the highest number of unknowns.
In the example above, 5x is larger than 3x.
Remove the unknowns on the other side by completing the inverse operation. To do this in this example you need to subtract 3x from both sides.
Now you can continue to balance the equation until you are left with the value of the unknown.
Solving equations
The balancing method can be used to solve equations as equations are like having a weighted scale which is balanced. If you take something off one side of the scale you must take the same thing off the other side to keep it balanced. This is the same for equations.
To solve an equation you have to find the value of the missing number which will be given a letter.
In this example you would subtract 3 from both sides to find the value of x is 2.
Solving equations with unknowns on one side
Remember to do the inverse operation on both sides
Finding the nth term
Remember your inverse operations………
Adding is the inverse of subtracting
Subtracting is the inverse of adding
Multiplying is the inverse of dividing
Dividing is the inverse of multiplying
Here is a sequence. 1, 4, 7, 10. The nth term is 3n-2.
To find the nth term you start by finding the common difference between terms. The picture demonstrate the rest of the method to find the nth term.
Key words and definitions
Equation – a mathematical statement that has two things equal to each other. It consists of two expressions either side of an equals sign.
Expression – in algebra this is a combination of terms
Term – the position in the sequence
Substitution – replacing letters with a given number
Sequence – a string of objects which follow a particular pattern. These can be pictures or numbers.
Pattern – when a picture or sets of numbers are in a specified sequence
nth term – an expression which will allow you to calculate a term that is in a particular position