The problem asks us to write two different equations based on the steps Angelina used for solving equations in the form $p(x + q) = r$. The steps mentioned are:

1. Divide the tiles into three equal groups on both sides of the mat.
2. Remove two groups from each side.
3. Add four 1-tiles to each side.

To align these steps with solving equations, here are two possible equations:

Equation 1:

1. Start with something like $3(x + 5) = 21$, where you have three groups of tiles (Step 1).
2. Divide both sides by 3: $x + 5 = 7$ (Step 1).
3. Remove $5$ from each side: $x = 2$.

Equation 2:

1. Start with something like $3(x + 1) = 18$, where you have three groups of tiles (Step 1).
2. Divide both sides by 3: $x + 1 = 6$ (Step 1).
3. Subtract $1$ from both sides: $x = 5$.

Would you like me to further elaborate on these equations or explore more examples?

Here are five related questions you might find useful:

1. How can you model the equation-solving process with physical objects like tiles?
2. How do the concepts of balancing and grouping relate to solving equations?
3. What happens when you divide or multiply both sides of an equation by the same number?
4. How can you write equations with larger coefficients or constants based on the steps?
5. What if an equation involves subtraction instead of addition?

Tip:

When solving equations, always perform the same operation on both sides to maintain equality!