Answer :
To solve the inequality [tex]\(-7 < x - 1 < 8\)[/tex], we need to isolate [tex]\(x\)[/tex]. Let's go through the steps together:
1. Start with the given inequality: [tex]\(-7 < x - 1 < 8\)[/tex].
2. Add 1 to each part of the inequality: This step helps us to isolate [tex]\(x\)[/tex] in the middle.
[tex]\[
-7 + 1 < x - 1 + 1 < 8 + 1
\][/tex]
3. Simplify each part:
[tex]\[
-6 < x < 9
\][/tex]
This tells us that [tex]\(x\)[/tex] is greater than [tex]\(-6\)[/tex] and less than [tex]\(9\)[/tex]. Therefore, the solution to the inequality is the interval:
[tex]\[
-6 < x < 9
\][/tex]
So the correct answer is [tex]\(-6 < x < 9\)[/tex].
1. Start with the given inequality: [tex]\(-7 < x - 1 < 8\)[/tex].
2. Add 1 to each part of the inequality: This step helps us to isolate [tex]\(x\)[/tex] in the middle.
[tex]\[
-7 + 1 < x - 1 + 1 < 8 + 1
\][/tex]
3. Simplify each part:
[tex]\[
-6 < x < 9
\][/tex]
This tells us that [tex]\(x\)[/tex] is greater than [tex]\(-6\)[/tex] and less than [tex]\(9\)[/tex]. Therefore, the solution to the inequality is the interval:
[tex]\[
-6 < x < 9
\][/tex]
So the correct answer is [tex]\(-6 < x < 9\)[/tex].
