Business Mathematics-1 Topic: Inequalities and absolute value—Distance on the Number Line

1. Business
Mathematics-1
_______________
Presentation
BY : ZOHAIB KHALID

2. Inequalities
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, >
‘greater than’, or < ‘less than’.
Examples of inequalities :
 5 < 7 ( 5 is less then 7 )
 X < 5 ( X is less then 5 )
 2x + 3 > 0 ( 2x + 3 is greater then or equal to 0 )

3. Roles of solving Inequalities
Inequalities are solved by using algebra and by using graphs.
When solving an inequality :
• you can add the same quantity to each side
• you can subtract the same quantity from each side
• you can multiply or divide each side by the same positive quantity
If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.

4. Solving Inequalities
Suppose we want to solve the inequality x + 3 > 2.
We can solve this by subtracting 3 from both sides:
x + 3 > 2
x > −1
So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2. Inequalities can be
represented on a number line such as that shown in given Figure . 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 equal −1.
A number line showing x > −1.

5. Example
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.
A number line showing x > 1.

6. Absolute Value—
Distance on the
Number Line

7. What is absolute value?
The absolute value of a number means the distance from 0.
Examples :
-5 is 5 units away from 0. So the absolute value of that -5 is 5. You cannot have negative distance, so
it must be positive.
 The symbol for absolute value is two straight lines surrounding the number or expression for which
you wish to indicate absolute value. |6| = 6 means the absolute value of 6 is 6.

8. What is a distance value?
The absolute value is the distance between two values, depending on the expression contained within
the absolute value sign. For example, the distance between two numbers x and y can be written as |x
– y|. Therefore: |x| = |x – 0| is the distance of x from 0.
Example :
 The absolute value of 2 + -7 is 5. Distance of sum from 0 : 5 units.
 The absolute value of 0 is 0. (This is why we don't say that the absolute value of a number is
positive: Zero is neither negative nor positive.)

9. Thank You!