To represent the inequality $25 - 4x > -7$ on a number line, let's first solve it.

Step 1: Solve for $x$

We begin by isolating $x$.

$25 - 4x > -7$

Subtract 25 from both sides:

$-4x > -7 - 25$

$-4x > -32$

Now, divide both sides by -4. When dividing by a negative number, remember to flip the inequality sign:

$x < \frac{-32}{-4}$

$x < 8$

Step 2: Represent $x < 8$ on a number line

• Draw a number line.
• Mark the point $8$ on it.
• Since the inequality is strict (i.e., $<$), we will use an open circle at $8$ to indicate that $8$ is not included.
• Shade all numbers to the left of 8 to represent $x < 8$.

Would you like me to generate a number line to visualize this solution?

Related Questions:

1. What is the process for solving inequalities that involve multiplication or division by negative numbers?
2. How do you represent solutions of inequalities that include "greater than or equal to" on a number line?
3. How does flipping the inequality sign work when dividing by negative numbers?
4. Can inequalities be solved using the same steps as equalities?
5. How do you solve compound inequalities?

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