Question

"Write the letter of the property that justifies each statement in the blank.

_15. If 4m + n = 7 and n = 3, then 4m + 3 = 7
A. Substitution Property

_16. If a = -5, then 2a = -10
E. Multiplication Property

_17. If 3x = y, then y = 3x
1. Symmetric Property

_18. If 4w – 1 = 11, then 4w = 12
B. Addition Property

_19. If a + b = c and c = d, then a + b = d
F. Transitive Property

_20. 6y = 6y
D. Reflexive Property

_21. If -8q = -56, then q = 7
G. Subtraction Property

_22. If 5k = -25, then 5k - 1 = -25 - 1
H. Distribution Property

_23. -3(2x - 5) = -6x + 15
H. Distribution Property"

Answer 1

The provided statements demonstrate various mathematical properties such as Substitution, Multiplication, Symmetric, Addition, Transitive, Reflexive, Division, Subtraction, and Distribution as solutions to the corresponding numbered statements.

Step-by-step explanation:

The answers to the given property identification questions for each statement are as follows:

1. Substitution Property: This property is used in statement 15 where n is replaced by 3 in the equation 4m + n = 7.
2. Multiplication Property: Statement 16 applies this property, showing that when a is -5, multiplying it by 2 gives -10.
3. Symmetric Property: In statement 17, the equation 3x = y can be rewritten as y = 3x, demonstrating symmetry.
4. Addition Property: In statement 18, the Addition Property is used to add 1 to both sides of the equation 4w – 1 = 11, yielding 4w = 12.
5. Transitive Property: Statement 19 illustrates the Transitive Property, where if a + b = c and c = d, then a + b = d.
6. Reflexive Property: Statement 20 shows that 6y is equal to itself, demonstrating the Reflexive Property.
7. Division Property: When the equation -8q = -56 is solved for q in statement 21, the Division Property is used to divide both sides by -8, obtaining q = 7.
8. Subtraction Property: In statement 22, subtracting 1 from both sides of the equation 5k = -25 results in 5k – 1 = -25 – 1.
9. Distribution Property: Statement 23 uses the Distribution Property as -3 is distributed over the terms within the parentheses, yielding -6x + 15.