https://file.aiquickdraw.com/mathbot/file/1726724138171nobq35u7.jpg

The inequality given in the image is:

\[
2x + 1 \leq 5 \quad \text{or} \quad 25 - 3x \leq 1
\]

Let's solve each inequality separately.

### 1st Inequality: \( 2x + 1 \leq 5 \)

- Subtract 1 from both sides:
  \[
  2x \leq 5 - 1
  \]
  \[
  2x \leq 4
  \]

- Divide both sides by 2:
  \[
  x \leq 2
  \]

### 2nd Inequality: \( 25 - 3x \leq 1 \)

- Subtract 25 from both sides:
  \[
  -3x \leq 1 - 25
  \]
  \[
  -3x \leq -24
  \]

- Divide both sides by \(-3\), and since we are dividing by a negative number, the inequality flips:
  \[
  x \geq 8
  \]

### Solution:

The solution is the union of the two inequalities, which is:

\[
x \leq 2 \quad \text{or} \quad x \geq 8
\]

So, the solution is all \(x\) such that \( x \leq 2 \) or \( x \geq 8 \).

Do you have any questions or would you like further explanation?

Here are 5 related questions you might be interested in:
1. How do you solve compound inequalities involving "and" instead of "or"?
2. What happens when inequalities contain fractions?
3. Can absolute value inequalities change the solution method?
4. How does solving quadratic inequalities differ from linear ones?
5. What are the graphical representations of compound inequalities?

**Tip**: When dividing or multiplying an inequality by a negative number, remember to flip the inequality sign.

Learn how to solve the compound inequalities 2x + 1 ≤ 5 or 25 - 3x ≤ 1 with step-by-step solutions. This problem covers key algebraic concepts, such as linear inequalities and the rule of flipping inequality signs. Suitable for students in Grades 9-10.

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