Fill in the Blank 5 points Solve the inequality. Use correct notation or "and" and "or". \( -1+|6+x| \geq 1 \)

Let's solve the inequality step by step! 1. Start by isolating the absolute value: \[ |6 + x| \geq 1 + 1 \] \[ |6 + x| \geq 2 \] 2. Now, we split this into two cases: Case 1: \( 6 + x \geq 2 \) Case 2: \( 6 + x \leq -2 \) 3. For Case 1: \[ 6 + x \geq 2 \] \[ x \geq 2 - 6 \] \[ x \geq -4 \] 4. For Case 2: \[ 6 + x \leq -2 \] \[ x \leq -2 - 6 \] \[ x \leq -8 \] Putting it all together, the solution in correct notation is: \[ x \leq -8 \text{ or } x \geq -4 \]