Question

If the replacement set is the set of integers, find the solution set for the inequality:

x−9<−15

A. {−8,−7,−6,…}
B. {−9,−8,−7,…}
C. {…,−8,−7,−6}
D. {…,−9,−8,−7}

Answer 1

To solve the inequality \( x - 9 < -15 \), we can start by isolating \( x \).

1. Add 9 to both sides of the inequality:
\[
x < -15 + 9
\]
Simplifying this gives:
\[
x < -6
\]

Now, the solution set includes all integers less than -6. This can be written in set notation as:

\[
\{..., -8, -7, -6\}
\]

Now let’s match this with the given options:

A. \{−8,−7,−6,…\} - This includes -6, which is not part of the solution since \( x \) must be less than -6.

B. \{−9,−8,−7,…\} - This includes all integers less than -6, so this works.

C. \{…,−8,−7,−6\} - This includes -6, which is not part of the solution.

D. \{…,−9,−8,−7\} - The lowest number included here is -7, which is less than -6, so this doesn't include integers more negative than -7.

Thus, the correct answer is:

**B. {−9,−8,−7,…}**