2. State the property that justifies each of the statements a) \( x(2)=2(x) \) b) \( (7+4)+6-7+(2+6) \) c) \( 1(x)=x \) d) \( \left(\frac{2}{3}\right)\left(\frac{3}{2}\right)=1 \)

a) This statement demonstrates the **Commutative Property of Multiplication**, which states that the order in which two numbers are multiplied does not affect the product. In this case, \( x(2)=2(x) \) shows that multiplying \( x \) by 2 is the same as multiplying \( 2 \) by \( x \). b) This expression illustrates the **Associative Property of Addition**, which states that the way in which numbers are grouped in an addition problem does not change their sum. Here, rearranging the grouping of numbers (as seen in \( (7+4)+6-7+(2+6) \)) will yield the same total regardless of how they are grouped. c) This statement reflects the **Multiplicative Identity Property**, which states that any number multiplied by 1 remains unchanged. The equation \( 1(x)=x \) confirms that multiplying \( x \) by the number 1 does not alter its value. d) This example highlights the **Multiplicative Inverse Property**, which states that the product of a number and its reciprocal (or multiplicative inverse) is always 1. In this case, \( \left(\frac{2}{3}\right)\left(\frac{3}{2}\right)=1 \) shows that when \( \frac{2}{3} \) is multiplied by \( \frac{3}{2} \), the result equals 1.