Which values are in the solution set of the compound inequality –8 < 3x + 7 ≤ 10? Select three options. –15 –5 –3 0 1
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andrewtrantu2008 7 months ago
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Step-by-step explanation:

–8 < 3x + 7 ≤ 10 That is the original compount inequality given.

We need to solve it in order to get an easy option.

-15, -5, -3, 0, 1 are the options.

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Steps to solve:

–8 < 3x + 7 ≤ 10

Subtract 7 from both sides

–8 < 3x ≤ 10 - 7

Now do 10-7

–8 < 3x ≤ 3

Do 3x divided by 3

–8 < x ≤ 1

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Evaluation and Answer Explanation:

–8 < x ≤ 1

That is your inequality statement.

The inequality statement states that "x" is greater than -8 but less than or equal to 1.

We can automatically choose 0 and 1 because 0 is greater than -8 and less than or equal to 1.

1 is correct because it is greater than -8 and less than or equal to 1

Now, there are two answers remaining: -15; -5.

Let's try -15.

-15 isn't greater than -8 but is less than 1. This is incorrect because it follows one inequality but doesn't follow both.

**Rule: the bigger you go on the negatives like -20 or -99 your numbers get smaller. If you go more towards the 0 like -1, -5, -3 your numbers get bigger.

-5 works because it is greater than -8 and less than or equal to 1.