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The problem asks you to solve the compound inequality:

\[
8x + 5 > 53 \quad \text{OR} \quad -1x + 3 \geq 6
\]

### Step 1: Solve each inequality separately.

#### First inequality: 
\[ 8x + 5 > 53 \]

Subtract 5 from both sides:
\[ 8x > 48 \]

Now, divide both sides by 8:
\[ x > 6 \]

#### Second inequality: 
\[ -1x + 3 \geq 6 \]

Subtract 3 from both sides:
\[ -1x \geq 3 \]

Now, divide both sides by -1. **Remember to flip the inequality sign** when dividing by a negative:
\[ x \leq -3 \]

### Step 2: Combine the two solutions using "OR".

- From the first inequality: \( x > 6 \)
- From the second inequality: \( x \leq -3 \)

The compound inequality is:
\[ x > 6 \quad \text{or} \quad x \leq -3 \]

### Step 3: Express the solution in interval notation.

In interval notation, the solution is:
\[
(-\infty, -3] \cup (6, \infty)
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How do you solve compound inequalities involving "AND"?
2. What happens if both inequalities have solutions that overlap?
3. Can a compound inequality ever have no solution? Why?
4. What is the difference between interval notation and set notation?
5. How do you handle inequalities with absolute values?

**Tip:** Always remember to flip the inequality sign when dividing or multiplying by a negative number!

Solve the compound inequality and give your answer in interval notation: 8x + 5 > 53 OR -1x + 3 ≥ 6.

Learn how to solve the compound inequality 8x + 5 > 53 OR -1x + 3 ≥ 6 with a step-by-step solution. This problem covers essential concepts like solving inequalities and using interval notation, perfect for students in Grades 7-9.

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