-7 os less than or equal to 2x + 1 < 11

To solve the compound inequality \(-7 \leq 2x + 1 < 11\), we can break it into two parts and solve each part separately.

1. Solve the left part: \(-7 \leq 2x + 1\)

   Subtract 1 from both sides: \[ -7 - 1 \leq 2x \] \[ -8 \leq 2x \]

   Now, divide by 2: \[ -4 \leq x \quad \text{or} \quad x \geq -4 \]

2. Solve the right part: \(2x + 1 < 11\)

   Subtract 1 from both sides: \[ 2x < 11 - 1 \] \[ 2x < 10 \]

   Now, divide by 2: \[ x < 5 \]

Now we combine the two results: \[ -4 \leq x < 5 \]

So the solution to the compound inequality \(-7 \leq 2x + 1 < 11\) is: \[ [-4, 5) \]