7. Solve each inequality and graph the solutions on a number line. Show your work. 

a.  



 

 

 

d.  LaTeX: 4x+7>23



### Let's solve the given inequality step by step:

#### Given Inequality:
\[
4x + 7 > 23
\]

#### Step 1: Subtract 7 from both sides
\[
4x + 7 - 7 > 23 - 7
\]
\[
4x > 16
\]

#### Step 2: Divide both sides by 4
\[
x > \frac{16}{4}
\]
\[
x > 4
\]

### Solution:
The solution to the inequality is:
\[
x > 4
\]

---

### Graphing on a Number Line:
1. Draw a horizontal line representing the number line.
2. Place a hollow/open circle at \(x = 4\) because the inequality is strict (\(>\), not \(\geq\)).
3. Shade the number line to the right of \(x = 4\), indicating all values greater than 4.

Would you like a visual representation of this graph? Let me know! 😊

---

### 5 Related Questions to Enhance Understanding:
1. How would the graph change if the inequality were \(4x + 7 \geq 23\)?
2. What is the solution if the inequality were \(4x + 7 < 23\)?
3. Can you write a similar inequality where \(x < 0\) and solve it?
4. How can inequalities be used to model real-world problems?
5. What is the difference in graphing \(x > 4\) versus \(x \geq 4\)?

### Tip:
Always pay attention to the inequality sign when solving and graphing inequalities to ensure you use the correct boundary (open or closed circle).

Solve each inequality and graph the solutions on a number line. Show your work. d. 4x + 7 > 23

Discover how to solve the inequality 4x + 7 > 23 step-by-step and learn how to graph its solution on a number line. This problem introduces key algebraic concepts like inequality properties and graphing techniques, suitable for Grades 6-8 students.

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