To solve the inequality [tex]\(-8 < x - 15\)[/tex], we need to isolate the variable [tex]\(x\)[/tex]. Here are the step-by-step instructions to achieve that:
1. Start with the given inequality:
[tex]\[
-8 < x - 15
\][/tex]
2. To isolate [tex]\(x\)[/tex], we need to eliminate the constant term on the right side of the inequality. We do this by adding 15 to both sides:
[tex]\[
-8 + 15 < x - 15 + 15
\][/tex]
3. Simplify both sides of the inequality. On the left side, we add [tex]\(-8\)[/tex] and 15, which gives 7. The right side simplifies as the [tex]\(-15\)[/tex] and [tex]\(+15\)[/tex] cancel each other out:
[tex]\[
7 < x
\][/tex]
4. The inequality [tex]\(7 < x\)[/tex] states that [tex]\(x\)[/tex] is greater than 7.
Therefore, the solution to the inequality [tex]\(-8 < x - 15\)[/tex] is:
[tex]\[
x > 7
\][/tex]
