Smith Davison
02/16/2023 · Middle School
Solve the compound inequality. \( -9 \leq x-2<-1 \) A. The solution set is \( \square \). (Type your answer in interval notation.) B. The solution set is the empty set.
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Step-by-step Solution
To solve the compound inequality \( -9 \leq x - 2 < -1 \), we can break it down into two parts and solve each part separately.
1. Solve the left part of the inequality:
\[
-9 \leq x - 2
\]
To isolate \( x \), add 2 to both sides:
\[
-9 + 2 \leq x
\]
\[
-7 \leq x
\]
This can be rewritten as:
\[
x \geq -7
\]
2. Solve the right part of the inequality:
\[
x - 2 < -1
\]
Again, add 2 to both sides:
\[
x < -1 + 2
\]
\[
x < 1
\]
Now we combine the two results:
\[
-7 \leq x < 1
\]
In interval notation, this solution set is:
\[
[-7, 1)
\]
Thus, the answer is:
A. The solution set is \( [-7, 1) \).
Quick Answer
The solution set is \( [-7, 1) \).
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