To solve the inequality $-4x + 29 > 19$, let's proceed step by step.

Step 1: Simplify the inequality

Subtract 29 from both sides:

$-4x + 29 - 29 > 19 - 29$

$-4x > -10$

Step 2: Solve for $x$

To isolate $x$, divide both sides by $-4$. Remember, dividing by a negative number reverses the inequality sign:

$x < \frac{-10}{-4}$

$x < 2.5$

Solution:

The inequality is $x < 2.5$. This represents all values less than 2.5.

On the number line, this would be shown as an open circle at 2.5 (because $x$ is less than 2.5, not equal to it), with the shading extending to the left to represent values smaller than 2.5.

Now, which number line best represents this?

Look for the option that shows:

• An open circle at 2.5
• A shaded line extending to the left of 2.5

Please let me know if you'd like any further clarification on this!

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Relative Questions:

1. What happens if we divide an inequality by a negative number?
2. How do we represent inequalities on a number line?
3. What would the solution be for the inequality $-4x + 29 \leq 19$?
4. Can you solve a similar inequality, like $-3x + 10 > 7$?
5. What if the inequality were $4x + 29 > 19$, how would that change the solution?

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