Question
Solve
\( -1
Ask by Murphy Murray. in the United States
Mar 16,2025
Ask by Murphy Murray. in the United States
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( -2 < x \leq 5 \).
Solution
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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Simplify this solution 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 \((-2, 5]\).
