Answer:
Commutative property:
a+b= b+a for any a and b
Multiplicative identity:
[tex]a \cdot 1 = 1 \cdot a[/tex] for any a.
Associative property:
a+(b+c) = (a+b)+c for any a, b and c
Distributive property:
[tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
Given the equation:
[tex](6x+3)-5x[/tex]
1.
Using commutative property:
[tex](3+6x)-5x[/tex]
2.
Using associative property.
[tex]3+(6x-5x)[/tex]
3.
Using distributive property:
[tex]3+(6-5)x[/tex]
4.
using subtraction.
[tex]3+(1)x[/tex]
5.
Using Multiplicative identity:
[tex]3+x[/tex]
Now, match each step with the property used to get to that step are as follow:
1. [tex](3+6x)-5x[/tex] [Commutative property]
2. [tex]3+(6x-5x)[/tex] [Associative property]
3. [tex]3+(6-5)x[/tex] [Distributive property]
4. [tex]3+(1)x[/tex] [Subtraction]
5. [tex]3+x[/tex] [Multiplicative property]
