What is the sum of all integers $n$ that satisfy $$-3n < 7n-20 < 3n~?$$

$($In other words, what is the sum of all integers $n$ that satisfy both of the inequalities
$$-3n<7n-20\text{~~and~~}7n-20&l t;3n~?)$$

If you can't figure out the latex here is a screenshot ( in the comments)

Looks like the inequality is

-3n < 7n - 20 < 3n

Add 3n to each side:

0 < 10n - 20 < 6n

Solve the right inequality.

10n - 20 < 6n

Add -10n to both sides:

-20 < -4n

Divides both sides by -4:

5 > n

Now solve the left inequality, and take the intersection of the two solution intervals.

0 < 10n - 20

Add 20 to both sides:

20 < 10n

Divide both sides by 10:

2 < n

So 2 < n < 5. There are only 2 integers in this range (3 and 4), whose sum is 7.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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