Answer :

To solve the inequality [tex]\(7 < 15 - x\)[/tex], we need to isolate the variable [tex]\(x\)[/tex]. Here's how you can do it step by step:

1. Start with the inequality:
[tex]\[
7 < 15 - x
\][/tex]

2. Subtract 15 from both sides to move the constant term:
[tex]\[
7 - 15 < -x
\][/tex]

3. Simplify the left side:
[tex]\[
-8 < -x
\][/tex]

4. We want to solve for [tex]\(x\)[/tex]. To do that, we multiply both sides by -1. Remember that when you multiply or divide an inequality by a negative number, you must reverse the inequality sign:
[tex]\[
8 > x
\][/tex]

5. Rearrange the solution to the more common notation:
[tex]\[
x < 8
\][/tex]

So, the solution to the inequality [tex]\(7 < 15 - x\)[/tex] is [tex]\(x < 8\)[/tex]. This means [tex]\(x\)[/tex] can be any number less than 8.

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