Answer :
Sure! Let's solve the inequality step by step.
We are given the inequality:
[tex]\[ -7 < x - 1 < 8 \][/tex]
Our goal is to solve for [tex]\( x \)[/tex].
### Step 1: Isolate [tex]\( x \)[/tex]
We start by isolating [tex]\( x \)[/tex] in the middle part of the inequality. To do this, we need to get rid of the [tex]\( -1 \)[/tex] that is subtracted from [tex]\( x \)[/tex].
To remove [tex]\( -1 \)[/tex], we will add 1 to all three parts of the inequality.
[tex]\[ -7 + 1 < x - 1 + 1 < 8 + 1 \][/tex]
### Step 2: Simplify the inequality
When we add 1 to each part, we simplify the inequality as follows:
[tex]\[ -7 + 1 = -6 \][/tex]
[tex]\[ x - 1 + 1 = x \][/tex]
[tex]\[ 8 + 1 = 9 \][/tex]
Putting it all together, we now have:
[tex]\[ -6 < x < 9 \][/tex]
### Conclusion
So the solution to the inequality [tex]\( -7 < x - 1 < 8 \)[/tex] is:
[tex]\[ -6 < x < 9 \][/tex]
This matches with the option [tex]\( -6 < x < 9 \)[/tex], which is the correct answer.
Therefore, the correct answer is [tex]\( -6 < x < 9 \)[/tex].
We are given the inequality:
[tex]\[ -7 < x - 1 < 8 \][/tex]
Our goal is to solve for [tex]\( x \)[/tex].
### Step 1: Isolate [tex]\( x \)[/tex]
We start by isolating [tex]\( x \)[/tex] in the middle part of the inequality. To do this, we need to get rid of the [tex]\( -1 \)[/tex] that is subtracted from [tex]\( x \)[/tex].
To remove [tex]\( -1 \)[/tex], we will add 1 to all three parts of the inequality.
[tex]\[ -7 + 1 < x - 1 + 1 < 8 + 1 \][/tex]
### Step 2: Simplify the inequality
When we add 1 to each part, we simplify the inequality as follows:
[tex]\[ -7 + 1 = -6 \][/tex]
[tex]\[ x - 1 + 1 = x \][/tex]
[tex]\[ 8 + 1 = 9 \][/tex]
Putting it all together, we now have:
[tex]\[ -6 < x < 9 \][/tex]
### Conclusion
So the solution to the inequality [tex]\( -7 < x - 1 < 8 \)[/tex] is:
[tex]\[ -6 < x < 9 \][/tex]
This matches with the option [tex]\( -6 < x < 9 \)[/tex], which is the correct answer.
Therefore, the correct answer is [tex]\( -6 < x < 9 \)[/tex].
