Match the property that justifies each statement.(7 points) Multiplication Property
Substitution Property
Reflexive Property
Symmetric Property
Addition Property
Subtraction Property
division property
If x = -5, then 2x = -10
If 5w - 1 = 11, then 5w = 12
If 6k=36, then 6k-1 = 36-1
If 5q = -55, then q = -11 8p = 8p
If 3m+n=7 and n=4, then 3m+4=7
If 4x = y, then y = 4x
1. Substitution Property
2. Addition Property
3. Subtraction Property
4. Substitution Property
5. Reflexive Property
6. Addition Property
7. Division Property
To match each statement with the corresponding property, let's examine each statement:
1. If x = -5, then 2x = -10
In this statement, the multiplication property is used. The multiplication property states that you can multiply both sides of an equation by the same number. In this case, we multiply x by 2 to get 2x and -5 by 2 to get -10.
2. If 5w - 1 = 11, then 5w = 12
Here the addition property is used. The addition property states that you can add the same value to both sides of an equation. In this case, we add 1 to both sides of the equation to isolate 5w.
3. If 6k = 36, then 6k - 1 = 36 - 1
Here we have the substitution property. The substitution property states that if two quantities are equal, you can substitute one for the other in any equation. In this case, we use the value of 6k from the first equation and substitute it into the second equation.
4. If 5q = -55, then q = -11
This is an example of the division property. The division property states that if you divide both sides of an equation by the same non-zero number, the equation remains true. In this case, we divide both sides of the equation by 5 to isolate the variable q.
5. 8p = 8p
This statement doesn't require any specific property to justify it. It is a reflexive property. The reflexive property states that any quantity is equal to itself.
6. If 3m + n = 7 and n = 4, then 3m + 4 = 7
Here we have the substitution property again. We substitute the value of n (which is known to be 4) into the first equation to obtain the second equation.
7. If 4x = y, then y = 4x
This is an example of the symmetric property. The symmetric property states that if a = b, then b = a. In this case, we can rewrite the equation as y = 4x, which is the same as 4x = y but written in a different order.
So, the matching properties for each statement are as follows:
1. Multiplication Property
2. Addition Property
3. Substitution Property
4. Division Property
5. Reflexive Property
6. Substitution Property
7. Symmetric Property
- Subtraction Property
- Addition Property
- Subtraction Property
- Division Property
- Reflexive Property
- Substitution Property
- Substitution Property