solve: 1) 3x+y=17, 2) 4x-y=18

1) 3x+y=17
2) 4x-y=18 

adding the two equations yields:
7x=35


thus
x=5 



now we can find y...
3*5+y=17
y=2

Factor: 15y^2+8y+1

since 3*5=15 and 3+5=8...


15y^2+8y+1=
15y^2+3y+5y+1=
(15y^2+3y)+(5y+1)=
3y(5y+1)+1(5y+1)=
(3y+1)(5y+1)

James is 4 years older than Kabul. In two years, their ages will total 50. How old is James now?

1) j-k=4
2) j+2+k+2=50 

j-k=4
j+k=46 

2j=50


j=25 

what is the truth value of the statement "2+4=6 and 9 is a prime number

Both statements are not true, so the and of them is not true. Thus the statement is false.

find two consecutive odd integers such that three times the smaller one exceeds two times the larger one by 7

1) n-m=2 <-- consecutive odds differ by 2
2) 3m+7=2n 



3(n-2)+7=2n
3n-6+7=2n
n=-1 
so m=-3

For what value of x is this inequality |x – 6|< - 8 true? Why?

for no value of x... 
|x – 6|< - 8 
has no solution because an absolute value of a real valued expression can never (by definition) be negative. Therefore it can never be less than -8

Curtis and Ben have 60 Marbles between them. how many do they each have if Curtis has 4 times as many as Ben

1) b+c=60
2) 4b=c 


so that...
5b=60 

and...
b=12
so we get: 
b=12, c=48