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Solve \( -1
Ask by Murphy Murray. in the United States
Mar 16,2025

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The solution is \( -2 < x \leq 5 \).

Solución

Given the inequality \[ -1 < x + 1 \leq 6, \] we can solve it in the following steps: 1. **Subtract 1 from all parts of the inequality.** Subtracting 1 from the left, middle, and right gives: \[ -1 - 1 < x + 1 - 1 \leq 6 - 1. \] 2. **Simplify each part.** This simplifies to: \[ -2 < x \leq 5. \] The solution to the inequality is: \[ x \in (-2, 5]. \]

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Bonus Knowledge

To solve the compound inequality \( -1 < x + 1 \leq 6 \), we first break it down into two parts: 1. From \( -1 < x + 1 \), we subtract 1 from both sides to get \( -2 < x \) or \( x > -2 \). 2. From \( x + 1 \leq 6 \), we also subtract 1 from both sides to obtain \( x \leq 5 \). Putting it all together, we have the solution: \(-2 < x \leq 5\) This can also be written in interval notation as \((-2, 5]\).

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