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Solve the inequality:

[tex] 7 \ < \ 15 - x [/tex]

Answer :

To solve the inequality [tex]\(7 < 15 - x\)[/tex], we need to find the values of [tex]\(x\)[/tex] that make this inequality true. Here's a step-by-step guide on how to solve it:

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

2. Isolate [tex]\(x\)[/tex]:
- Begin by subtracting 15 from both sides to help isolate [tex]\(x\)[/tex]. When you do this, the inequality becomes:
[tex]\[
7 - 15 < -x
\][/tex]
- Simplifying the left side gives:
[tex]\[
-8 < -x
\][/tex]

3. Reverse the inequality:
- To eliminate the negative sign in front of [tex]\(x\)[/tex], multiply both sides of the inequality by [tex]\(-1\)[/tex]. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. So:
[tex]\[
8 > x
\][/tex]

4. Rewrite the solution:
- The inequality [tex]\(8 > x\)[/tex] is usually written as:
[tex]\[
x < 8
\][/tex]

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

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