PtLSV

Before we learn PtLSV, we should be understand the definition of statement sentence and open sentence.
1. statement sentence
Sentence which could have been properly defined right or wrong is called sentence statement.
Example : a. Many soccer players in one team is 11 people (right)
b. Currency of UK is Dollar (wrong)
2. open sentence
Sentence which could not determine whether the sentence is right or wrong is called open sentence.
Example : "9 reduced by one number the result is a 5". If a number is replaced with x, then the sentence could be written in mathematical symbols 9 - x = 5.
We can not determine whether the sentence is right or wrong, because " a number " in the sentence is not known value yet.
3. definition of linier
The open sentence which use connected symbol “=” is called equation. If the highest exponent of variable one equation is one so that equation is called linier equation. Linier equation only have one variable is called linier equation one variable (PLSV).
Replacement of variables (changer) so that a correct equation is right called settlement equation , while a set of load all referred to the settlement is called collective settlement.
Example and method :
• 20 – x = 17
-x = 17 – 20 ( 20 remove to right segment so become -20 )
-x = -3
x = 3 ( each other multiply by -1)
HP = { 3 }
• x – 5 = 4
x = 4 + 5 ( 5 remove to right segment so become -5)
x = 9
HP = { 9 }
• 8 + 4n = 20
4n = 20 – 8 ( 8 remove to right segment so become -8)
4n = 12
4n (1/4) = 12 (1/4)
n = 3
HP = { 3 }
• 3x + 5 = 2x + 3
3x + 5 – 5 = 2x + 3 – 5 ( each segment reduce by 5)
3x = 2x – 2
3x – 2x = 2x – 2x – 2 ( each segment reduce by 2x)
x = - 2
HP = {-2}
4. Definition of linier unequation one variable
Linier unequation one variable is mathematic sentence which load one variable one exponent and load symbol not equivalent( >, ≥ , ≤ ).
The settlement of linier equation is variable value interval which memenuhi that unequation. To Determine linier unequation one variable by determine the simplest equivalent form from that unequation.
Unequation will be equivalent if :
a. both segment added / reduced with same number.
b. both segment multiplied / divided with same positive number.
c. both segment multiplied / divided with same negative number and followed with substitute unequation symbol.

 graphic of unequation settlement set :










Examples and the method :
• X > 13 ( x | x is circle number )
HP = { 14, 15, 16, 17, … }
• A ≤ 6 ( a | a is real number)
HP = { 1, 2, 3, 4, 5}
• 3a – 6 < 9
3a – 6 + 6 < 9 + 6 ( both segment added by 6)
3a < 15
3a ( 1/3) < 15 (1/3)
a < 5
HP = { …, 1, 2, 3, 4}
 Determine equivalent form from PtLSV
Determine equivalent form from PtLSV (By the both segment added, reduced, multiplied, and divided by the same number). Of course you still remember about the equivalent equation, namely equation which have same settlement set. Similarly the equivalent unequation, namely unequation which have same settlement set.


Example and the method :
1. 3x – 9 > 6
2. 3x > 15
If changer in no 1 and 2 is { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, so :
• Settlement set from 3x – 9 > 6 is { 6, 7, 8, 9 10 }
• Settlement set from 3x > 15 is { 6, 7, 8, 9, 10 }. So 3x – 9 > 6 equivalent 3x > 15

 Determine equivalent form from PtLSV with method each segment added / reduced with same number.
1. if each segment added by 4, so obtained:
2 > -3
2 + 4 > -3 + 4
6 > 1 ( right statement)
2. if each segment reduced by 1, obtained :
2 > -3
2 – 1 > -3 – 1
1 > -4 ( right statement)

 Determine equivalent form from PtLSV with method both segment multiplied / divided with same number.
Look at statement 4 < 10 is right statement.
• Multiplied or divided with same positive number
1) 4 x 3 < 10 x 3 ( both segment multiplied by 3)
12 < 30 ( right statement)
2) 4 : 2 < 10 : 2 (both segment divided by 2 )
2 < 5 ( right statement)
• Multiplied or divided with same negative number.
1) 4 x (-3) < 10 x (-3) ( both segment multiplied by -3)
-12 < -30 ( wrong statement)
right is ; -12 > -30
2) 4 : (-2) < 10 : (-2) ( both segment divided by -2)
-2 < -5 (wrong statement)
the right is -2 > -5


EXERCISES
1. what is open sentences ? give an example!
Answer :


2. what is statement sentences ? give an example !
Answer :


3. what is linier equation one variable ? give an example !
Answer :


4. what is linier unequation one variable ? give an example !
Answer :


5. give ‘R’ for right and ‘W’ from wrong from which one is unequation!







6. make each two equivalent unequation with :
a. 4y – 12 < 8
answer :


b. 6a + 9 > -15
answer :


7. Are the couples of equation is equivalent?
a. 2y + 16 = 20 with 2y = 4 ( )
b. 3x – 5 = 7 with x = 5 ( )
c. 8n + 12 = 5n – 6 with 3n = -18 ( )
8. look at this mathematic sentences !

From that sentences which one is PtLSV? Give a reason!
Answer :








9. Make 5 PtLSV with some forms and variables !
Answer :


10. Determine settlement set with changer {-5,-4,-3,-2,-1,0,1,2 ,3,4,5} !
a. x – 3 < 1
b. 5 – 3p ≥ - 4
c. 13 – 3x > 18 – 8x
Answer :
a. x – 3 + …. < 1 + …
x < ……

HP = {……………………………}
b. 5 – 5 – 3p ≥ ………
- 3p (…) ≥ ………
p ……………
HP = {……………………………}
c. 13 - … – 3x > 18 - … – 8x
- 3x >…………….
- 3x + 8x >…………….
… ( 1/5 ) >……( 1/5 )
x >…….
HP= {……………………………}
11. A circle number multiplied by 4 than added by 12, and the result is -8. determine that number ! (note : make that number with x)
answer :

12. The sum of 4 ganjil numbers is 56.
a. if first number is n, declare second, third, and fourth number in n!
b. arrange the equation in n and finish it!
c. determine the value from that four number!
Answer :
a.

b.

c.

13. Found the HP from – 6x ≥ 13 – x for x Є circle number set.
Answer :
3 - … – 6x ≥ 13 - … - x
- 6x ≥ … - x
- 6x + … ≥ 10
- 5x (…) ≥ 10 (…)
x ……. -2
HP = {…………………………}
14. Found the HP from 2(3x – 4) – 3(4 –3x) < 10, x Є R !
Answer :
2( … ) + 2( … ) – 3 ( … ) – 3 ( … ) < 10
6x – … – 12 + … < 10
15x - … < 10
15x < 10 + …
15x ( … ) < … ( … )
x < …
HP = { x | x………, x Є R}
15. Found the HP from 5x + 20 < 8 + 7x , x Є R !
Answer : 5x + 20 – … < 8 – … + 7x
5x + 12 < 7x
5x – … < …
… < -12
-2x ( … ) < -12 ( … )
………………..
x………
HP = { x | ………, x Є R}