Answer :

To solve the inequality [tex]\(6 < x - 6 \leq 9\)[/tex], follow these steps:

1. Identify the inequality: We have the compound inequality [tex]\(6 < x - 6 \leq 9\)[/tex]. Our goal is to solve for [tex]\(x\)[/tex].

2. Add 6 to all parts of the inequality: To isolate [tex]\(x\)[/tex], we need to eliminate the [tex]\(-6\)[/tex] next to it. We do this by adding 6 to each part of the inequality:

[tex]\[
6 + 6 < x - 6 + 6 \leq 9 + 6
\][/tex]

3. Simplify: This gives us:

[tex]\[
12 < x \leq 15
\][/tex]

So the solution to the inequality is that [tex]\(x\)[/tex] is greater than 12 and less than or equal to 15.

This means [tex]\(x\)[/tex] can be any value between 12 and 15, but not including 12 itself. However, 15 is included in the range of possible values for [tex]\(x\)[/tex].

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Rewritten by : Barada