What is the sum of all integers $n$ that satisfy $$-3n < 7n-20 < 3n~?$$ $($In other words, what is the sum of all in

Question

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
$$-3n<7n-20\text{~~and~~}7n-20<3n~?)$$

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

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Bơ 4 years 2021-09-01T22:25:18+00:00 1 Answers 7 views 0

Answers ( )

  1. dangkhoa
    0
    2021-09-01T22:26:50+00:00
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    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.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )