Use properties of equality to solve the following equations. Identify the properties used and describe their application. 6. (-5 × 7) × 25 = x × (7 × 25) 7. 5x = 0 8. 63 = 1x 9. (1/8)x = 1 10. 65 × 92 × 17 = 92 × 17 × x

6. The equation given is (-5 × 7) × 25 = x × (7 × 25). We can start solving this by using the Associative Property of Multiplication, which states that the way in which factors are grouped does not affect the product:

(-5 × 7) × 25 = (7 × 25) × x

Now, since both sides have (7 × 25), we can divide both sides by (7 × 25) to solve for x using the Division Property of Equality. This property states when both sides of the equation are divided by the same nonzero number, the sides remain equal:

(-5 × 7) × 25 / (7 × 25) = x × (7 × 25) / (7 × 25) -5 = x

The solution is x = -5.

7. The equation given is 5x = 0. The Multiplication Property of Zero states that any number multiplied by zero gives zero. So, applying the Division Property of Equality to both sides we get:

5x / 5 = 0 / 5 x = 0

The solution is x = 0.

8. The equation given is 63 = 1x. The Multiplicative Identity Property states that any number multiplied by 1 is the number itself. So, 1x is just x:

x = 63

The solution is x = 63.

9. The equation given is (1/8)x = 1. In this case, to solve for x, we can use the Multiplication Property of Equality by multiplying both sides by the reciprocal of 1/8:

(1/8)x * (8/1) = 1 * (8/1) x = 8

The solution is x = 8.

10. The equation given is 65 × 92 × 17 = 92 × 17 × x. Here, we can use the Commutative Property of Multiplication, which states that we can swap the order of multiplication without changing the result:

65 × 92 × 17 = 92 × 17 × x

Since 92 × 17 is common on both sides, we divide both sides by 92 × 17 to isolate x, using the Division Property of Equality:

(65 × 92 × 17) / (92 × 17) = (92 × 17 × x) / (92 × 17) 65 = x

The solution is x = 65.