Use properties of equality to solve these equations. Identify the properties used and describe how you used them.
22. (–5 • 7)25 = x(7 • 25)
23. 5x = 0
24. 63 = 1x
25.
26. 65 • 92 • 17 = 92 • 17 • x
22. By using the commutative property of multiplication, we can rearrange the equation to: (7 • -5) • 25 = (7 • 25) • x. Then, by using the associative property of multiplication, we can further simplify the equation to: -35 • 25 = 7 • 25 • x. Since -35 • 25 is equal to -875 and 7 • 25 is equal to 175, we have: -875 = 175x. Finally, by dividing both sides of the equation by 175, we find that x = -5. The properties used in this equation are the commutative property of multiplication and the associative property of multiplication.
23. To solve this equation, we need to isolate the variable by using the multiplicative identity property. We can divide both sides of the equation by 5, resulting in x = 0/5, which simplifies to x = 0. The property used in this equation is the multiplicative identity property.
24. We can solve this equation by using the multiplicative identity property. Since any number multiplied by 1 is itself, we have x = 63 • 1, which simplifies to x = 63. The property used in this equation is the multiplicative identity property.
25. The equation provided is incomplete and cannot be solved.
26. By using the commutative property of multiplication, we can rearrange the equation to: 65 • 92 • 17 = 92 • 17 • x. Then, by dividing both sides of the equation by 92 • 17, we find that x = 65. The property used in this equation is the commutative property of multiplication.