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If 5(4 − x) < y + 12 and y + 12 < 3x + 1, then which statement is true?

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Answer:

To determine which statement is true based on the given inequalities, let's analyze each inequality separately and then compare the results.

Given inequalities:

1. 5(4 - x) < y + 12

2. y + 12 < 3x + 1

Let's start with the first inequality:

1. 5(4 - x) < y + 12

We can simplify it by distributing the 5 on the left side:

20 - 5x < y + 12

Next, let's consider the second inequality:

2. y + 12 < 3x + 1

We can rearrange it to isolate y:

y < 3x + 1 - 12

y < 3x - 11

Now, let's compare the two results:

20 - 5x < y + 12

y < 3x - 11

From these inequalities, we can see that the second statement, "y < 3x - 11," is true.

To summarize, based on the given inequalities, the statement "y < 3x - 11" is true.

Explanation:

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