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.