Question

Solve: `-7\le2x+1<11`

Answer 1

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:
1. \(x \geq -4\)
2. \(x < 5\)

Combining these, we get:
\[
-4 \leq x < 5
\]

### Final Answer
The solution in interval notation is:
\[
[-4, 5)
\]