**RPH**

Class : 3A1 (32
students)

Date : 10

^{th}August 2011
Day
: Wednesday

Week : 12

^{th}Week
Time : 80
minutes (7.35-8.55 a.m.)

Topic : Linear Inequalities

Learning Area : Linear Inequalities

Learning Outcome : 1. Identify relationship

a. greater
than

b. less
than

c. using
a symbol / sign “> “or “ <” and “≥ “or” ≤

2. Identify the relationship between 2 given
number

a.
greater than or equal to

b.
less than or equal to base on given situation

Learning Objectives : 1. Students be able to understand and use
the concept of inequalities

2. Students be able to understand and use the concept of linear

Inequalities in one unknown

3. Understand the sign “> “or “ <” and
“≥ “or” ≤

Learning Activities :

Let a, b and c be real numbers.

- Transitive Property

If a < b and b < c then a < c - Addition Property

If a < b then a + c < b + c - Subtraction Property

If a < b then a - c < b - c - Multiplication
Property
- If
a < b and c is positive then c*a < c*b
- If
a < b and c is negative c*a > c*b

Note:

- If each inequality sign is
reversed in the above properties, we obtain similar properties.
- If the inequality sign < is
replaced by <= ( less than or equal) or the sign > is replaced by
>= ( greater than or equal ), we also obtain similar properties.

**Solve****2***x*__<__**9.**

If given "2

*x*= 9", should have divided the 2 from each side. can do the same thing here:
Then
the solution is:

*x*__<__^{9}/_{2}
...or,
if you prefer decimals (and if your instructor will accept decimal equivalents
instead of fractions):

*x*

__<__

**4.5**

**Solve**/^{x}_{4}>^{1}/_{2}.

If
they had given "

*/*^{ x}_{4}=^{1}/_{2}", have multiplied both sides by 4. I can do the same thing here:
Then
the solution is:

*x*> 2**Solve –2***x*< 5.

Remember
how I said that solving linear inequalities is "almost" exactly like
solving linear equations? Well, this is the one place where it's different. To
explain what I'm about to do, consider the following:

3
> 2

What
happens to the above inequality when I multiply through by –1? The
temptation is to say that the answer will be "–3 > –2".
But –3 is not

*greater*than –2; it is in actuality*smaller*. That is, the correct inequality is actually the following:
–3
< –2

As
you can see, multiplying by a negative ("–1", in this case) flipped
the inequality sign from "greater than" to "less than".
This is the new wrinkle for solving inequalities:

When solving inequalities, if multiply or divide
through by a negative, must also flip the inequality sign.

To
solve "–2

*x*< 5", I need to divide through by a negative ("–2"), so I will need to flip the inequality:
Then
the solution is:

*x*>^{–5}/_{2}**Solve**^{(2x – 3)}/_{4}__<__**2.**

First,
I'll multiply through by 4. Since the "4" is positive, I don't
have to flip the inequality sign:

^{(2x – 3)}/

_{4}

__<__2

(4) ×

^{(2x – 3)}/

_{4}

__<__(4)(2)

2

*x*– 3

__<__8

2

*x*

__<__11

*x*__<__

^{11}/_{2}= 5.5
Achievement : 1. Student must know
the difference of the sign

2. Ask the selected student to answer the
question one by one

3. Student is able to answer the question

Reflection : Student knows how
to state the numbers by one unknown in linear inequalities.

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