Topic Five: "Inequality"
Introduction:
The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by anarrowhead. It is an example of an inequality.
This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3. We
will be interested in finding the values of x for which the inequality is true.
We use four symbols to denote inequalities:
Key Point
> is greater than
> is greater than or equal to
< is less than
< is less than or equal to
EXAMPLES:
1. We can solve this by subtracting 3 from both sides:
x + 3 > 2
x > −1
Inequalities can be represented on a number line such as that shown in Figure 1. The solid line
shows the range of values that x can take. We put an open circle at −1 to show that although
the solid line goes from −1, x cannot actually equal −1.
Figure 1. A number line showing x > −1.
2. Suppose we wish to solve the inequality
4x + 6 > 3x + 7.
First we subtract 6 from both sides to give
4x > 3x + 1
Now we subtract 3x from both sides:
x > 1
This is the solution. It can be represented on the number line as shown in Figure 2.
Figure 2. A number line showing x > 1.
REFERENCE:
www.mathcentre.ac.uk/resources/uploaded/mc-ty-inequalities-2009-1.pdf
No comments:
Post a Comment