Inequality Symbols

1
(No Transcript)
2

• Inequality Symbols

3
Linear Inequalities
Examples of linear inequalities
These inequalities can be solved like linear
equations EXCEPT that multiplying or dividing by
a negative number reverses the inequality.
Consider the numbers 1 and 2
Dividing by -1 gives -1 and -2
BUT -1 is greater than -2
-1
-2
1
2
4
Linear Inequalities
Examples of linear inequalities
These inequalities can be solved like linear
equations EXCEPT that multiplying or dividing by
a negative number reverses the inequality.
Consider the numbers 1 and 2
Dividing by -1 gives -1 and -2
BUT -1 is greater than -2
The inequality has been reversed
5
Solution
Divide by 3
e.g.2 Find the range of values of x that satisfy
the inequality
Solution Collect the like terms
Notice the change from less than to greater
than
Divide by -4

• Collecting the x-terms on the side which makes
  the coefficient positive avoids the need to
  divide by a negative number

• Substitute one value of x as a check on the answer

6
Exercises
Find the range of values of x satisfying the
following linear inequalities
1.
Solution
2.
Solution Either
so,
Or
Divide by -4
7
Quadratic Inequalities
Solution
Method ALWAYS use a sketch
Rearrange to get zero on one side
The corresponding x values are between -3 and 1
8
Solution
There are 2 sets of values of x
These represent 2 separate intervals and CANNOT
be combined
9
e.g.3 Find the values of x that satisfy
Solution
This quadratic has a common factor, x
10
SUMMARY

• Linear inequalities

Solve as for linear equations BUT

• Keep the inequality sign throughout the working

• If multiplying or dividing by a negative number,
  reverse the inequality

• Quadratic ( or other ) Inequalities

• rearrange to get zero on one side, find the zeros
  and sketch the function

• Use the sketch to find the x-values satisfying
  the inequality

• Dont attempt to combine inequalities that
  describe 2 or more separate intervals

11
Exercise
Solution
There are 2 sets of values of x which cannot be
combined
12
Exercises
Find the solution set of x ? R 1. 5x-3 3x5 2.
2x1 gt 5x7 3. 4. 1 2x-1 5 5. 6.
13
(No Transcript)
14

• LKS PAGE 49 SOAL LATIHAN Number 1,3,6,10

15
The following slides contain repeats of
information on earlier slides, shown without
colour, so that they can be printed and
photocopied.
For most purposes the slides can be printed as
Handouts with up to 6 slides per sheet.
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)