Question

Solve the compound inequality.
6 less than x plus 8 less than 8
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set in interval notation is
  
enter your response here.
B.
The solution is empty set.

Answer 1

To solve the compound inequality given by:

\[ 6 < x + 8 < 8 \]

we can break it down into two separate inequalities:

1. \( 6 < x + 8 \)
2. \( x + 8 < 8 \)

### Solving the first inequality:

1. \( 6 < x + 8 \)

Subtract 8 from both sides:

\[ 6 - 8 < x \]

\[ -2 < x \]

Or, equivalently:

\[ x > -2 \]

### Solving the second inequality:

2. \( x + 8 < 8 \)

Subtract 8 from both sides:

\[ x < 8 - 8 \]

\[ x < 0 \]

### Putting it all together:

Now we combine the results from both inequalities:

\[ -2 < x < 0 \]

### Writing in interval notation:

The solution set in interval notation is:

\[ (-2, 0) \]

### Final Answer:

A. The solution set in interval notation is \((-2, 0)\).