To solve the compound inequality \(-7 \leq 2x + 1 < 11\), we can break it down into two separate inequalities and solve each part step by step.
Step 1: Solve the left part of the inequality
\[ -7 \leq 2x + 1 \] Subtract 1 from both sides: \[ -7 - 1 \leq 2x \] \[ -8 \leq 2x \] Now, divide both sides by 2: \[ -4 \leq x \quad \text{or} \quad x \geq -4 \]
Step 2: Solve the right part of the inequality
\[ 2x + 1 < 11 \] Subtract 1 from both sides: \[ 2x < 11 - 1 \] \[ 2x < 10 \] Now, divide both sides by 2: \[ x < 5 \]
Step 3: Combine the results
We have two inequalities:
- \(x \geq -4\)
- \(x < 5\)
Combining these, we get: \[ -4 \leq x < 5 \]
Final Answer
The solution in interval notation is: \[ [-4, 5) \]