https://file.aiquickdraw.com/mathbot/file/172804208885604ez7pzm.jpg

The given image represents a double inequality:

\[
15 \leq 2x + 1 < 7
\]

Let's solve this inequality step-by-step.

### Step 1: Break the Compound Inequality
The given compound inequality can be broken into two parts:

1. \( 15 \leq 2x + 1 \)
2. \( 2x + 1 < 7 \)

### Step 2: Solve Each Part

#### Part 1: \( 15 \leq 2x + 1 \)

Subtract 1 from both sides:

\[
15 - 1 \leq 2x
\]

\[
14 \leq 2x
\]

Divide by 2:

\[
7 \leq x
\]

or equivalently:

\[
x \geq 7
\]

#### Part 2: \( 2x + 1 < 7 \)

Subtract 1 from both sides:

\[
2x < 6
\]

Divide by 2:

\[
x < 3
\]

### Step 3: Combine the Results

We have two inequalities for \(x\):

\[
x \geq 7 \quad \text{and} \quad x < 3
\]

It is clear that there is no possible value of \(x\) that satisfies both conditions simultaneously. Therefore, **there is no solution** to the given inequality.

### Summary
The inequality \( 15 \leq 2x + 1 < 7 \) has no solution.

Would you like more details on this, or do you have any questions?

Here are some related questions that you might find helpful:

1. How do you solve compound inequalities with overlapping ranges?
2. What is the difference between "and" and "or" in inequalities?
3. How can you graph inequalities on a number line?
4. How do you interpret inequalities with "less than or equal to" and "strictly less than"?
5. What does it mean if a compound inequality has no solution?

**Tip:** When solving compound inequalities, always break them into parts and solve each part independently before combining the results.

Learn how to solve the compound inequality 15 ≤ 2x + 1 < 7 with a detailed step-by-step solution. This problem involves key algebraic concepts such as solving linear inequalities and understanding compound inequalities. Suitable for students in Grades 8-10.

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