The symbol

is used to indicate that the quantity on the left of the < is smaller than the quantity to the right. The inequality corresponds to the English statements:- is less than ,
*not*be equal to .)
is smaller than . (Note that this means that can

The symbol *or equal to* the quantity to the right. The inequality corresponds to the English statements:

- is less than or equal to ,
*can*be equal to .)
is at most . (Note that this means that

The symbol

is used to indicate that the quantity on the left of the < is smaller than the quantity to the right. The inequality corresponds to the English statements:- is greater than ,
*not*be equal to .)
is more than . (Note that this means that can

The symbol *or equal to* the quantity to the right. The inequality corresponds to the English statements:

- is greater than or equal to ,
*can*be equal to .)
is at least . (Note that this means that

The *closed interval* is the section of the number line between and inclusive. It corresponds to the set values of where .

The *open interval* is the section of the number line between and exclusive. It corresponds to the set of values of where .

The *interval* is the section of the number line between inclusive and exclusive. It corresponds to the set of values of where .

The *interval* is the section of the number line between exclusive and inclusive. It corresponds to the set of values of where .

The *unbounded intervals* , , , correspond to the set of values of given by the following inequalities:

corresponds to the set of values of given by ,

corresponds to the set of values of given by ,

corresponds to the set of values of given by ,

corresponds to the set of values of given by ,

corresponds to the set of real numbers.

The real number line is a horizontal line with a zero at the centre where everything to the left of zero is negative numbers and everything to the right is positive numbers. Every real number has exactly one position on the line and every position on the line corresponds to a real number.

Number lines are useful for visualising set of real numbers, interval and values of

satisfying an inequality.An interval is a subset of the real numbers corresponding to a section of the number line. The endpoints may or may not be included, for example

is the interval from -3 (inclusive) to 2 (exclusive). THe square brackets indicates that the first number is included, and indicates that it is excluded. Similarly for and for the second number.Inequalities are relationships between quantities or expressions where one is less than, less than or equal to, greater than or greater than or equal to the other.

Linear inequalities involve one variable, and that variable does not occur as

or any higher exponent.