Question

1. Simplify: (2n-3)/(6n-9) A) 3 B) 1 C) 1/3 D) 1/3n


2. Multiply: (4x+12)/(x^2-2x) × x/(6x+18) A) 2/(3(x-2)) B) 2/(x-2) C) 2/3 D) 4/x


3. Subtract: 8x/(x+1)- 3/(x+1) A) 5x/(x+1) B) (8x-3)/(x+1) C) 5 D) 5x


4. Simplify: (9x3 + 15x2 + 6x) ÷ (3x + 4) A) 3x2 B) 3 + x C) 3x2 + x + 2x/(3x+4) D) x + 2/3


5. Solve: 1/2+ 3/t = 5/8 A) t = 1 B) t = 2/3 C) t = 1/6 D) t = 24


6. Solve: 5/(2x-3)= 7/3x A) x = 21 B) x = -21 C) x = 2/3 D) x = (-2)/3


7. Write an equation for the inverse variation. y = 7 when x = 3. A) y = 21 B) x = 21 C) y = 21/x D) x = 21y


8. Mark can clean his father’s office in 30 minutes. His younger sister Lynn can clean the office in 40 minutes. How long will it take the two of them together to clean the office? (3 points) Answer = minutes

Answer 1

the answers:
1) simplification:
(2n-3)/(6n-9)=(2n-3)/3(2n-3), because (6n-9)=3(2n-3),
(2n-3)/(6n-9)=(2n-3)/3(2n-3) =1/3 (simplified by (2n-3))
the answer is C) 1/3
2) multiplication
(4x+12)/(x^2-2x) × x/(6x+18), the rule is a/b x c/d = axc /bxd
(4x+12)/(x^2-2x) × x/(6x+18)= x (4x+12) / (x^2-2x) (6x+18)
= x (4x+12) / x (x -2) (6x+18)= (4x+12) / (x -2) (6x+18) (simplified by x)
but we know that 6x+18=6(x+3) and 4(x+3)
then (4x+12) / (x -2) (6x+18)=4(x+3)  / (x -2)6(x+3)= 4/ 6 (x-2) (simplified by x+3)
so it is  2/(3(x-2)) and the answer is A) 2/(3(x-2))
3) substraction
8x/(x+1)- 3/(x+1) = 8x -3 / (x+1) the main rule a/b - c/ b= a-c / b
the answer is B) (8x-3)/(x+1)
4) simiplification
(9x3 + 15x2 + 6x) ÷ (3x + 4) = ?, the answer is C) 3x2 + x + 2x/(3x+4) 

proof   3x2 + x + 2x/(3x+4) = (3x2 + x )(3x+4) + 2x / 3x +4=9x^3 + 12x² +3x²+4x +2x / 3x+4= 9x3 + 15x2 + 6x) / 3x +4

5)  1/2+ 3/t = 5/8, for solving it, just place 1/2 in the second member, and pay attention to the change of sign
 3/t = 5/8 - 1/2 =10 - 8 / 16 = 2/16= 1/8, and 3/t = 1/8, and it is equivalent t/3=8/1=8, so t= 24. D) t = 24 
6)  5/(2x-3)= 7/3x
main rule
a/b=c/d is equivalent to axd =bxc 

5/(2x-3)= 7/3x is equivalent to 7(2x-3) = 5(3x) and it is 14x -21 = 15x
for soving it we have to do as follow
14x-15x= 21, and -x = 21 finally x= -21 answer B) x = -21
7) y = 7 when x = 3
the equation is C) y = 21/x, because y=21/3= 7
8) the answer is
40mn + 30 mn  / 2 =  35 mn