Which number line best represents the solution to the inequality -4x + 29 > 19?

To solve the inequality \(-4x + 29 > 19\), follow these steps:

1. **Isolate the variable \(x\):**

   Start by subtracting 29 from both sides:

   \[
   -4x + 29 - 29 > 19 - 29
   \]
   \[
   -4x > -10
   \]

2. **Solve for \(x\):**

   Divide both sides by \(-4\), and remember to reverse the inequality sign since you're dividing by a negative number:

   \[
   x < \frac{-10}{-4}
   \]
   \[
   x < 2.5
   \]

The solution to the inequality is \(x < 2.5\).

### Number Line Representation:
On a number line, the solution would be represented as all values to the **left** of \(2.5\), with an **open circle** at \(2.5\) to indicate that \(2.5\) itself is not included in the solution.

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Do you need more details or have any questions?

Here are 5 related questions:

1. How do you represent inequalities graphically on a number line?
2. What happens to the inequality sign when dividing by a negative number?
3. Can you explain when to use open or closed circles on a number line?
4. What are some real-life applications of inequalities?
5. How would you solve a similar inequality with a greater or equal sign?

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

Learn how to solve the inequality -4x + 29 > 19 and represent the solution on a number line. This step-by-step guide covers essential algebraic techniques and highlights the rule of flipping the inequality sign when dividing by a negative number. Suitable for Grades 6-8 students.

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