Year 10 Interactive Maths - Second Edition

## Solving Inequalities

Linear inequalities are also called first degree inequalities, as the highest power of the variable (or pronumeral) in these inequalities is 1.

E.g.  4x > 20 is an inequality of the first degree, which is often called a linear inequality.

Many problems can be solved using linear inequalities.

We know that a linear equation with one pronumeral has only one value for the solution that holds true. For example, the linear equation 6x = 24 is a true statement only when x = 4. However, the linear inequality 6x > 24 is satisfied when x > 4. So, there are many values of x which will satisfy the inequality 6x > 24.

Similarly, we can show that all numbers greater than 4 satisfy this inequality.

## Inequalities Involving One Operation

###### Recall that:
• the same number can be subtracted from both sides of an inequality
• the same number can be added to both sides of an inequality
• both sides of an inequality can be multiplied (or divided) by the same positive number
• if an inequality is multiplied (or divided) by the same negative number, then:

### Subtracting a Number from Each Side of an Inequality

Subtracting a number from each side of an inequality does not change the sign of the inequality.

#### Example 21

##### Solution:

###### Note:

(i)  The solution set consists of all numbers greater than 4, and is shown on the number line as follows:

The ring at 4 in this diagram means that 4 is not an element of the solution set.

#### Example 22

##### Solution:

###### Note:

(i)  The solution set consists of all numbers less than or equal to –2, as shown on the following number line.

The solid dot at –2 in the diagram means that –2 is an element of the solution set.