Algebra

Question 1

equivalent transformation of inequality: x> y + a

Answer 1

x + a > y +a

Question 2

important inequality with absolute values

Answer 2

|X + Y| <= |X| + |Y|

Question 3

sequence

Answer 3

a list of objects separated by comma

Question 4

arithmetic sequence (what is it)

Answer 4

An=A1 + d(n-1); d - common difference = An-An-1

Question 5

the same of the first n terms of an arithmetic sequence

Answer 5

Sn=(A1+An)/2 X n or Sn=(2A1+d(n-1))/2 X n

Question 6

geometric sequence

Answer 6

the riot between any two consecutive terms is the same.

An/An-1 = Q; An=An-1 X Q

Question 7

geometric sequence of nth term

Answer 7

An=A1 X Q^(n-1)

Question 8

sometimes a problem will provide two inequalities and ask you to combine them in some way

Answer 8

How to solve:
2 < X < 5; 3 
find max and min:
5-3=2 (max)
2-3=-1
2-10= -8 (min)
5-10= -5
Finally: -8

Question 9

absolute values: if a >0

Answer 9

|X|=a -> X = a or X= -a.

Question 10

absolute values: if |X| < a

Answer 10

-a -3 0

Question 11

absolute values: if |X| > a

Answer 11

or X>A or X |X-3| > 3 -> X-3>3 or X-3 or X>6 or X<0

Question 12

Sqroot of X^2?

Answer 12

|X|