Question

Solve for d.
2≤d+17<8
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 2 \leq d + 17 < 8 \), we will break it down into two parts.

1. **Solve the left part**:
\[
2 \leq d + 17
\]
Subtract 17 from both sides:
\[
2 - 17 \leq d
\]
\[
-15 \leq d
\]
This can be written as:
\[
d \geq -15
\]

2. **Solve the right part**:
\[
d + 17 < 8
\]
Subtract 17 from both sides:
\[
d < 8 - 17
\]
\[
d < -9
\]

Now, combining both parts, we have:
\[
-15 \leq d < -9
\]

Thus, the solution in compound inequality form is:
\[
-15 \leq d < -9
\]

To express this with integers only, the integer solutions for \( d \) are:
\[
d = -15, -14, -13, -12, -11, -10
\]

In conclusion, the compound inequality is:
\[
-15 \leq d < -9
\] with integer solutions of \( d = -15, -14, -13, -12, -11, -10 \).