1. Name the property that Justifies each step in the simplification below.
1/2[(x+2)+(-x)]=1/2[-x+(x+2)] a.__?__
=1 /2[(-x=x)+2)] b.__?__
= 1/2(0+2) c.__?__
= 1/2*2 d.__?__
=1 e.__?__
My answers
a. Communitive Property
b.Assotiative Property
c. equavelent expression
d. Multiplication Property
E. i don't know
I don't think that all my answers r right can you please help me!!!!!
a,b,c look ok
d: where is the multiplication? I think equivalent again, since 0+2=2
e: also not sure. no transformation is invilved; just straight multiplication.
You did a great job with the first four steps! Let's review your answers:
a. Commutative Property: This property states that you can change the order of addition or multiplication without changing the result. In this case, you switched the order of (x + 2) and (-x) by changing it to (-x) + (x + 2). So, your answer is correct.
b. Associative Property: This property states that you can change the grouping of numbers when adding or multiplying without changing the result. In this case, you changed the grouping of (-x) + (x + 2) to (-x + x) + 2. So, your answer is also correct.
c. Equivalent Expression: This is not a property but a concept. Equivalent expressions have the same value, even though they may look different. In this step, you transformed (-x + x) + 2 to 0 + 2, which are equivalent expressions.
d. Multiplication Property: This property allows you to multiply a number by 1 without changing its value. In this step, you multiplied 1/2 by 2. So, your answer is correct.
e. Unit Value: In the final step, you can see that 1/2 multiplied by 2 equals 1. So, the answer is 1. We can call this the "Unit Value" because multiplying any number by 1 does not change its value.
Therefore, your answers for the first four steps are correct, and for the final step, the name of the property is "Unit Value". Great job!