Let's break down the mats and solve the expressions for each:

Symbols:

• The small shaded square represents +1.
• The small unshaded square represents -1.
• The large shaded rectangle represents +x.
• The large unshaded rectangle represents -x.

Mat A:

• Top section: There is 1 small shaded square (+1), 1 large shaded rectangle (+x), and 1 small unshaded square (-1).
• Bottom section: There are 2 large shaded rectangles (+x) and 1 small shaded square (+1).

So the expression for Mat A would be: $A = (1 - 1 + x) + (x + x + 1)$ Simplifying: $A = (x) + (2x + 1)$ $A = 3x + 1$

Mat B:

• Top section: There is 1 small shaded square (+1) and 1 large shaded rectangle (+x).
• Bottom section: There is 1 large shaded rectangle (+x).

So the expression for Mat B would be: $B = (x + 1) + (x)$ Simplifying: $B = x + 1 + x$ $B = 2x + 1$

Comparing the two:

• Expression for Mat A: 3x + 1
• Expression for Mat B: 2x + 1

Since the two constants are the same, we only need to compare the coefficients of $x$. Since $3x > 2x$, Mat A is greater.

Would you like more details on any step or have additional questions?

Here are 5 relative questions:

1. How would the comparison change if the constant term in Mat B were larger?
2. What happens if you subtract a constant from both mats?
3. How do legal moves affect simplification?
4. Can both mats be balanced or equal under any conditions?
5. How would negative values for $x$ affect the result?

Tip: When simplifying expressions, always group like terms first for easier comparison.