Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.15

2.2 INEQUATIONS

An inequality is a sort of equation. With an equation you calculate when two formulas are equal. With an
inequality you calculate when one of the formulas is less (or greater) than the other formula. This of course
has everything to do with the point(s) of intersection of the two formulas.
You have to know the meaning of the different signs being used.
Examples
x + 5 > 4x + 7.
3 x + 7 < 20x
Solving linear inequalities is the same as solving linear equations with one very important exception ——
when you multiply or divide an inequality by a negative value, it changes the direction of the inequality.
SYMBOL MEANING
Before we begin our example problems, refresh your memory < less than
on what each inequality symbol means. It is helpful > greater than
to remember that the “open” part of the inequality ≤ less than or equal to
symbol (the larger part) always faces the larger quantity. ≥ greater than or equal to

Solving single linear inequalities follow pretty much the same process for solving linear equations. We will
simplify both sides, get all the terms with the variable on one side and the numbers on the other side, and
then multiply/divide both sides by the coefficient of the variable to get the solution. The one thing that
you’ve got to remember is that if you multiply/divide by a negative number then switch the direction of
the inequality.

SOLVED EXAMPLES
Example 18 :

Solve the inequality^2 x 3 x 5 − ≥ 2 − 1

Solution:

2 x 3 x 1

5 2

− ≥ −

(10)

2 x 3 (10) 1x

5 2

− (^) ≥ (^) −
(^)
4x – 6 ≥ 5x – 10
4x – 6 – 5x + 6 ≥ 5x – 10 – 5x + 6

• x ≥ -4
  x 4
  1 1

− ≤−

− −

x ≤ 4

Example 19 :
Solve the inequality 4(x + 1) < 2x + 3