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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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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