Everything Maths Grade 10

Solve 2 x+ 2 = 1:

2 x+ 2 = 1

2 x= 1 2

2 x= 1

x=

1

2

If we represent this answer on a number line, we get:

 3  2  1 0 1 2 3

x=^12

Now let us solve forxin the inequality 2 x+ 2 1 :

2 x+ 2 1

2 x 1  2

2 x 1

x

1

2

If we represent this answer on a number line, we get:

 3  2  1 0 1 2 3

x^12

We see that for the equation there is only a single value ofxfor which the equation is true. However, for the
inequality, there is a range of values for which the inequality is true. This is the main difference between an
equation and an inequality.

Remember:when we divide or multiply both sides of an inequality by a negative number, the direction of the
inequality changes. For example, ifx < 1 , thenx > 1. Also note that we cannot divide or multiply by a
variable.

NOTE:

The following video provides an introduction to linear inequalities.

See video:2FGHatwww.everythingmaths.co.za

Interval notation EMA3J

Examples:

(4; 12) Round brackets indicate that the number is not included. This interval includes all real

numbers greater than but not equal to 4 and less than but not equal to 12.

(1;1) Round brackets are always used for positive and negative infinity. This interval includes

all real numbers less than, but not equal to1.

[1; 13) A square bracket indicates that the number is included. This interval includes all real

numbers greater than or equal to 1 and less than but not equal to 13.

It is important to note that this notation can only be used to represent an interval of real numbers.

We represent the above answer in interval notation as

(

1;^12

]

Chapter 4. Equations and inequalities 97