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(4). Solve the equation (3X – 2) = 10
(a). 4 and -8/3 (b). 2 and -4/3 (c). -4 and 2/3
Choose any number in the option and if it gives zero as the answer then the option is correct.
Checking Option A
Make X = 4
Solution Using Casio fx991es
[ON] [4] [SHIFT] [STO] [X] [AC] [(] [3] [ALPHA] [X] [-] [2] [)] [-] [(] [1] [0] [)] [=]
In this case I tried plus it didn’t give zero as the answer then I tried minus and it gives zero as the answer therefore it is correct.
Make X = -8/3
Solution Using Casio fx991es
[ON] [-] [8] [÷] [3] [=] [SHIFT] [STO] [X] [AC] [(] [3] [ALPHA] [X] [-] [2] [)] [+] [(] [1] [0] [)] [=]
In this case I tried minus it didn’t give zero as the answer then I tried plus and it gives zero as the answer, Therefore Option A is correct.
You can go ahead and try other Option to see if it is correct.

(5). Find the solution set of the inequalities X² – 3X + 2 > 0
(a). 1 < X < 2 (b) -1 < X < -2 (c). -2 < X < -3
Choose any number in the option and if it gives zero as the answer then the option is correct.
Checking Option A
Make X = 1
Solution Using Casio fx991es
[ON] [1] [SHIFT] [STO] [X] [AC] [(] [ALPHA] [X] [X²] [-] [3] [ALPHA] [X] [+] [2] [)] [+] [(] [0] [)] [=]
In this case I used plus sign it gives zero as the answer and I used minus sign it still gives zero as the answer so both of them are correct.
Make X = 2
Solution Using Casio fx991es
[ON] [2] [SHIFT] [STO] [X] [AC] [(] [ALPHA] [X] [X²] [-] [3] [ALPHA] [X] [+] [2] [)] [-] [(] [0] [)] [=]
In this case I used plus it gives zero as the answer and I used minus it still gives zero as the answer, so you can use any of them both of them are correct as far as it gives zero as the answer. Therefore Option A is correct.

CALCULATOR METHOD TO SOLVE PARTIAL FRACTION:::

PARTIAL FRACTION
(1). Express 5x –12/
(x – 2)(x – 3)
(A) 2 – 2 (B) 2 + 3
(C) 2 – 3 (D) 5 – 2
(x – 2) (x – 3) (x – 2) (x – 3 ) (x – 3) (x – 2) (x – 2) (x – 2)
Solution:-Using CASIO fx-991MS calculator.
Make X= any number (1, 2, 3, ……….100) or more.
Apart from the numbers given to you in partial
Fraction and after solving and you are getting the
Same value (answer) from the options and from the
Question then the option is correct. It can be applied
On calculator fx 991es.
I am using X to be 9 {X=9}
[ON] [9] [SHIFT] [STO] [X] (x=9)
–when dividing the numerator and the denominator put brackets to avoid errors when using CASIO fx-991MS calculator except it is a whole number i.e.
“(5x – 4)”/
“((x – 2)(x – 2))”
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [(] [5] [ALPHA] [X] [-] [1] [2] [)] [a b / c ] [(] [(] [ALPHA] [X] [-] [2] [)] [(] [ALPHA] [X] [-] [3] [)] [)] [=] ( 11 / 14 )
Checking option A, B, C, D if any of the option gives 11 / 14 it is correct but if it didn’t give 11 /14 it is wrong
Checking option (A) 2 – 2/
(x – 2) (x – 3)
[AC] [2] [a b / c ] [(] [ALPHA] [X] [-] [2] [)] [-] [3] [a b / c ] [(] [ALPHA] [X] [-] [3] [)] [=] (- 3 / 14 )
Option (A) is wrong because it did not give 11 /14
Checking option (B) 2 + 3/
(x – 2) (x – 3)
[AC] [2] [a b / c ] [(] [ALPHA] [X] [-] [2] [)] [+] [3] [a b / c] [(] [ALPHA] [X] [-] [3] [)] [)] [=] ( 11 / 14 )
Option (B) is correct because it give
11 /14
Checking option (C) 2 – 3/
(x – 3) (x – 2)
[AC] [5] [a b / c ] [(] [(] [ALPHA] [X] [-] [3] [)] [-] [4] [a b / c ] [(] [ALPHA] [X] [-] [2] [)] [)] [=] ( 11 / 42 )
Checking option (D) 5 – 2/
(x – 2) (x – 3)
[AC] [5] [a b / c ] [(] [(] [ALPHA] [X] [-] [3] [)] [-] [4] [a b / c ] [(] [ALPHA] [X] [-] [2] [)] [)] [=] ( 1 / 14 )
Option (D) is wrong because it did not give 11 /14
(2). Express 1 as a partial fraction
x 3 – 1
(A) 1 / 3 { 1 / X – 1 – X – 2 / X2 – X + 1 } (B) 1 / 3 { 1 / X – 1 – X + 2 / X 2 + X + 1 } (C) 1 / 3 { 1 / X – 1 – X – 2 / X2 – X + 1 } (D) 1 / 3 { 1 / X – 1 – X + 2 / X2 – X – 1 }
Solution:-Using CASIO fx-991MS calculator make x = any number of your choice i.e. x = 9
[ON] [9] [SHIFT] [STO] [X] (X=9)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [1] [a b / c ] [(] [ALPHA] [X] [x 3 ] [-] [1] [)] [=] ( 1 / 728 )
Checking option A, B, C, D if any of the option gives 1 /728 it is corret but if it didn’t give 1/728 it is wrong
Checking (A) 1/ 3{ 1 / X – 1 – X – 2/ X2 – X + 1 }
–when dividing the numerator and denominator put brackets to avoid error when using CASIO fx-991MS calculator except it is a whole numbers
i.e. “( 1 /3 { 1 /(X – 1) – (X – 2) /(X 2 – X + 1) }”
[AC] [1] [a b / c ] [3] [(] [1] [a b / c ] [(] [ALPHA] [X] [-] [1] [)] [-] [(] [ALPHA] [X] [-] [2] [)] [a b / c ] [(] [ALPHA] [X] [x 2 ] [-] [ALPHA] [X] [+] [1] [)] [)] [=] (17 / 1752)
Option (A) is wrong because it did not give 1/728
Checking (B) 1 / 3{ 1/ X – 1 – X + 2 / X2 + X + 1 }
–when dividing the numerator and denominator put brackets to avoid error when using CASIO fx-991MS calculator except it is a whole numbers
[AC] [1] [a b / c] [3] [(] [1] [a b / c ] [(] [ALPHA] [X] [-] [1] [)] [-] [(] [ALPHA] [X] [+] [2] [)] [a b / c] [(] [ALPHA] [X] [x 2 ] [+] [ALPHA] [X] [+] [1] [)] [)] [=] (1 / 728)
Option (B) is correct because it give
1/728
Checking (C) 1 / 3{ 1/ X – 1 – X – 2 / X2 +
x + 1 }
–when dividing the numerator and denominator put brackets to avoid error when using CASIO fx-991MS calculator except it is a whole numbers
[AC] [1] [a b / c ] [3] [(] [1] [a b / c ] [(] [ALPHA] [X] [-] [1] [)] [-] [(] [ALPHA] [X] [-] [2] [)] [a b / c ] [(] [ALPHA] [X] [x 2 ] [+] [ALPHA] [X] [+] [1] [)] [)] [=] (5 / 312)
Option (C) is wrong because it did not give 1/728
Checking (D) 1 / 3{ 1/ X – 1 – X + 2 / X2 – X – 1}
–when dividing the numerator and denominator put brackets to avoid error when using CASIO fx-991MS calculator except it is a whole numbers
[AC] [1] [a b / c ] [3] [(] [1] [a b / c ] [(] [ALPHA] [X] [-] [1] [)] [-] [(] [ALPHA] [X] [-] [2] [)] [a b / c ] [(] [ALPHA] [X] [x 2 ] [-] [ALPHA] [X] [+] [1] [)] [)] [=] (- 17 / 1704 )
Option (D) is wrong because it did not give 1/728

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