Solve for d.

Question

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 \( d = -15, -14, -13, -12, -11, -10 \).