The problem asks us to compare two mathematical expressions and insert the correct inequality or equality sign ($>$, $<$, or $=$) between them. We need to do this for three pairs of expressions.

1. Problem Description

The problem asks us to compare two mathematical expressions and insert the correct inequality or equality sign ($>$, $<$, or $=$) between them. We need to do this for three pairs of expressions.

2. Solution Steps

First expression: $(10+5)-9$ vs $(10+9)-5$

* Evaluate the left expression: $10 + 5 = 15$, then $15 - 9 = 6$.

* Evaluate the right expression: $10 + 9 = 19$, then $19 - 5 = 14$.

* Compare: $6 < 14$.

Second expression: $3 \times (4+5)$ vs $(3 \times 4) + 5$

* Evaluate the left expression: $4 + 5 = 9$, then $3 \times 9 = 27$.

* Evaluate the right expression: $3 \times 4 = 12$, then $12 + 5 = 17$.

* Compare: $27 > 17$.

Third expression: $(10 \times 4) + 2$ vs $10 \times (4+2)$

* Evaluate the left expression: $10 \times 4 = 40$, then $40 + 2 = 42$.

* Evaluate the right expression: $4 + 2 = 6$, then $10 \times 6 = 60$.

* Compare: $42 < 60$.

3. Final Answer

$<$

$>$

$<$