JSS 1 Mathematics Third Term Week 3
Topic: SIMPLE EQUATIONS
Do you go blank when you see x, y and z in mathematics? Well, this is your abc to solving equations.
Solving simple equations
In an equation, letters stand for a missing number. To solve an equation, find the values of missing numbers. A typical exam question is:
Solve the equation 2a + 3 = 7
This means we need to find the value of a. The answer is a = 2
There are two methods you can use when solving this type of problem:
Trial and improvement
Using inverses
Trial and improvement
This method involves trying different values until we find one that works.
Look at the equation 2a + 3 = 7
To solve it:
Write down the equation: 2a +3 = 7
Then, choose a value for ‘a’ that looks about right and work out the equation. Try ‘3’.
a = 3, so 2 ×3 + 3 = 9.
Using ‘3’ to represent ‘a’ makes the calculation more than 7, so choose a smaller number for ‘a’.
Try a = 2
2 × 2 + 3 = 7
Which gives the right answer. So a = 2
Be systematic in your approach:
- choose a number
- work it out
- then move the number up or down
However, sometimes the answers are negatives or decimal fractions, and the trialand improvement method will take a long time. Luckily, there is a better method.
Using inverses
The best way to solve an equation is by using ‘inverses’, or undoing what the equation is doing.
To use this method to solve equations remember that:
Adding and subtracting are the inverse (or opposite) of each other.
Multiplying and dividing are the inverse of each other.
This method is explained in the following pages. But for now, here is how to solve the question in the above example using inverses:
First, write down the expression:
2a + 3 = 7
Then, undo the + 3 by subtracting 3. Remember, you need to do it to BOTH sides!
2a + 3 – 3 = 7 – 3,
so 2a = 4.
Undo the multiply by 2 by dividing by 2, again on both sides:
2a ÷ 2 = 4 ÷ 2
The answer is: a = 2
Solution of an equation
It is usually possible to find the value of the unknown which makes an equation true. We call this value the solution of the equation.
x = 6 is the solution of 3x = 18.
To solve an equation means to find its solution.
Example
Solve the equation 18 – x = 7
The problem is to find a number which when taken from 18 gives 7. The number is 11.
x = 11 is the solution
Find the solution of 3x = 15.
Which number multiplied by 3 gives 15? The number is 5. Thus
x = 5.
Exercise
Solve the following equations
1. 20 + x = 28
2. 14 – x = 11
3. x – 2 = 15
4. 4x = 20
5. 3x + 4 = 17