Solve for k. 10 ≤ k + 11 < 20 Write your answer as a compound inequality with integers. Choices: (A)-1 ≤ k < 31 (B)-1 ≤ k < 9 (C)21 ≤ k < 31 (D)21 ≤ k < 9

Analyze Compound Inequality: Analyze the given compound inequality. The inequality 10 ≤ k + 11 < 20 involves two inequalities combined: one is ＂10 ≤ k + 11＂ and the other is ＂k + 11 < 20＂. We need to isolate k in both inequalities.Subtract to Isolate k: Subtract 11 from all parts of the compound inequality to isolate k. 10 - 11 ≤ k + 11 - 11 < 20 - 11 -1 ≤ k < 9Check Solution: Check the solution against the provided choices. The solution we found is ＂-1 ≤ k < 9＂, which matches choice (B).

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

k

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10 \leq k + 11 < 20

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

-1 \leq k < 31

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(B)

-1 \leq k < 9

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(C)

21 \leq k < 31

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(D)

21 \leq k < 9

Analyze Compound Inequality: Analyze the given compound inequality. $\newline$ The inequality 10 \leq k + 11 < 20 involves two inequalities combined: one is $10 \leq k + 11$ and the other is k + 11 < 20. We need to isolate $k$ in both inequalities.
Subtract to Isolate $k$ : Subtract $11$ from all parts of the compound inequality to isolate $k$ .10 - 11 \leq k + 11 - 11 < 20 - 11-1 \leq k < 9
Check Solution: Check the solution against the provided choices. $\newline$ The solution we found is -1 \leq k < 9, which matches choice $(B)$ .