Solve.

Question

−1 < x + 1 ≤ 6
Responses
A 0 < x ≤ 5
B 2 < x ≤ 5
C −5 < x < 0
D −2 < x ≤ 5

Answer 1

To solve the compound inequality \(-1 < x + 1 \leq 6\), we need to break it down into two separate inequalities and solve each one.

1. Solve the first part: \(-1 < x + 1\)

Subtract 1 from both sides:
\[
-1 - 1 < x + 1 - 1
\]
\[
-2 < x
\]

2. Solve the second part: \(x + 1 \leq 6\)

Subtract 1 from both sides:
\[
x + 1 - 1 \leq 6 - 1
\]
\[
x \leq 5
\]

Now combine both results:
\[
-2 < x \leq 5
\]

So, the solution to the compound inequality \(-1 < x + 1 \leq 6\) is \(-2 < x \leq 5\).

The correct response is:
D \(-2 < x \leq 5\)

Answer 2

check again

Answer 3

Let's re-evaluate the compound inequality \(-1 < x + 1 \leq 6\) step-by-step:

1. Split the compound inequality into two parts and solve each part separately.

\[ -1 < x + 1 \]

Subtract 1 from both sides:

\[ -1 - 1 < x + 1 - 1 \]

\[ -2 < x \]

So, the first part of the inequality simplifies to:

\[ x > -2 \]

2. Solve the second part:

\[ x + 1 \leq 6 \]

Subtract 1 from both sides:

\[ x + 1 - 1 \leq 6 - 1 \]

\[ x \leq 5 \]

Now, combine both parts:

\[ -2 < x \leq 5 \]

This simplifies to:

\[ -2 < x \leq 5 \]

Therefore, the correct answer is indeed:

D. \(-2 < x \leq 5\)