solve each inequality  graph solution set on the number line 
3a+8<23 or 1/4a - 6 >7

Let's solve each inequality step by step:

### 1st inequality:  
\[ 3a + 8 < 23 \]

#### Steps:
1. Subtract 8 from both sides:
   \[
   3a < 23 - 8
   \]
   \[
   3a < 15
   \]

2. Divide both sides by 3:
   \[
   a < \frac{15}{3}
   \]
   \[
   a < 5
   \]

### 2nd inequality:
\[ \frac{1}{4}a - 6 > 7 \]

#### Steps:
1. Add 6 to both sides:
   \[
   \frac{1}{4}a > 7 + 6
   \]
   \[
   \frac{1}{4}a > 13
   \]

2. Multiply both sides by 4:
   \[
   a > 13 \times 4
   \]
   \[
   a > 52
   \]

### Combined solution:
The solution set is:
- \( a < 5 \) (from the first inequality), OR
- \( a > 52 \) (from the second inequality).

### Graph on the number line:
- Draw an open circle at \( a = 5 \) and shade to the left for \( a < 5 \).
- Draw an open circle at \( a = 52 \) and shade to the right for \( a > 52 \).

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Would you like a detailed graph, or do you have any questions about the solution?

Here are some related questions:
1. How do you solve compound inequalities involving both "and" and "or"?
2. What are the differences between strict inequalities and non-strict inequalities?
3. How do you graph inequalities on a number line that include equal signs?
4. How do you solve inequalities that include fractions?
5. How do you interpret inequalities in real-world problems?

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

solve each inequality graph solution set on the number line 3a+8<23 or 1/4a - 6 >7

Learn how to solve and graph inequalities like 3a + 8 < 23 or 1/4a - 6 > 7 with a detailed step-by-step solution. This problem involves algebraic inequalities and graphing techniques, making it suitable for students in Grades 7-9.

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