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.