help with algebra problems?

Question

1. Twice the sum of two consecutive integers is 13 less than 5 times the smaller integer.. Find the larger integer.
2. Suppose n is a nonzero real number. Which of the ff. is always true?
a. |n|>n b. -|n|>-n c. 1/|n|>0 d. none of the above
3. How many integral values of k are there for w/c x^2+kx+12 is factorable?
a. 0 b. 3 c. 6 d. none of the above
4. Express the ratio of 4h:36min in the simples form.
a. 4/35 b. 48/7 c. 7/48 d. 35/4
5. A boat travels upstream at 17km/h. The same boat travels downstream at 37km/h. Find the rate of the current.
a. 10km/h b. 27km/h c. 20km/h d. n.o.t.a
6. the equation x^2+2x+5=0 has how many real roots?
a. 0 b. 1 c. 2 d. 3
7. W/c of the ff must be true for all real numbers?
I. x-y= y-x II. -(-x)=x III. x(y-z)=xy-xz
a. I only b. II only c. III only d. II and III only
8. W/c of the ff is true for 2a+b=a?
a. a=b b. a=-b c. 2a=a+b d. 3a=b

Answer 1

1:
2(a+a+1)=5a-13
2a+2a+2=5a-13
4a+2=5a-13
15=a (the smaller interger)
16= larger interger


5:
b=boat speed in still water
c=current speed
b+c=37
b -c=17
2b =54 (adding the two equations to eliminate c)
b=27
27+c=37
c=10 km/h

7: d
8: b

Answer 2

1. let first integer be x. so 2nd integer = x+1
2(x+x+1)+13=5x
4x + 2 + 13 = 5x
15 = 5x-4x
x = 15
so, larger integer = x+1=15+1=16

2.c. (i think )

4. (d)
5. let the speed of the stream be yand boat be x
so,
x-y=17
x+y = 37
2x =54
x= 27
replacing x,
27 + y=37
y=10 kmph
The speed of stream is 10kmph


7 (d).
8. (b)


Hope it helped!

Answer 3

1.first integer=x So the next integer is x+1 here we have:
2(x+x+1)+13=5x =>simple it 4x+2+13=5x =>x=15
2.d is correct because 1 is positive and InI is positive too so 1/InI is positive so it's more than 0.

Answer 4

2(x + x+1)+13 = 5x

the larger integer is x + 1

good luck