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polet [3.4K]
3 years ago
10

The greatest integer that satisfies the inequality 1.6−(3−2y)<5

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
6 0

Solve the inequality 1.6-(3-2y)<5.

1. Rewrite this inequality without brackets:

1.6-3+2y<5.

2. Separate terms with y and without y in different sides of inequality:

2y<5-1.6+3,

2y<6.4.

3. Divide this inequality by 2:

y<3.2

4. The greatest integer that satisfies this inequality is 3.

Answer: 3.

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Explanation:

Let's go over an example.

We'll have a = 1 and b = 7 which makes a < b true. Feel free to pick your own favorite pair of numbers such that b is larger than 'a'.

The corresponding opposites are:  -a = -1 and -b = -7

The relationship flips because the opposites of each number are flipped. So instead of saying -a < -b, we have -a > -b

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In short, going from a < b to -a > -b means we flip the signs of each term, and we flip the inequality sign as well.

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