Solve for z.

Question

12>z+5≥0
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 12 > z + 5 \geq 0 \), we'll break it down into two parts.

1. Solve the left part of the inequality:
   \( 12 > z + 5 \)

   Subtract 5 from both sides: \[ 12 - 5 > z \] \[ 7 > z \quad \text{or} \quad z < 7 \]

2. Solve the right part of the inequality:
   \( z + 5 \geq 0 \)

   Subtract 5 from both sides: \[ z \geq -5 \]

Combining both parts gives us the compound inequality: \[ -5 \leq z < 7 \]

In summary, the solution in the form of a compound inequality is: \[ -5 \leq z < 7 \]