Match the expressions with thier equivalent equations in the columns.

List A: List B:
6x+12 6(1+x)
6+6x 6x-6
6(x-1) 6(x+2)
Fill in the blank:
The expression 6x+12 is equivalent to the expression __________
The expression 6+6x is equivalent to the expression __________
The expression 6(x-1) is equivalent to the expression __________

Noted:
So, I don't understand this because the problem is not saying what is variable x is, ( for example, y= 5, n=3 or b=8) *something like that*.
So, I don't know how to solve it or how to answer this problem. I also need help with the fill-in the blanks since i first don't know how to solve the expressions above.

Note: If anyone can help, that would be appreciated.

What I need from you:
- explaining (first)
on how to solve this problem
*this would also help a lot when I come across a problem (hopefully, in the future) like this then I am already prepared to solve the problem*
- answers (goes with explaining as well)
*to see the correct answers of the expressions (in the lists A and B)
and the fill-in blanks*

Note: If you don't understand on what I am asking then hopefully I can explaining it better to you when I respond back. (or read carefully on what I am saying and asking)

Own Words:
Sorry for asking too much but this will help me a lot.

In conclusion:
Thanks for helping!

Also the expressions are List A is seperated from expressions on List B.

Sorry for puting the lists all together but I hope you understand.

No value for x is needed. This is an exercise in recognizing the distributive property.

5(x+3) = 5*x + 5*3 = 5x+15

Now see what you can do.

Oh thanks! Now, I get it and thanks for the help. I can do this on my own now.

*sorry* my name is nathaly but I like to put my name shorter for nat...

To solve this problem, we need to determine the equivalent equations for each expression in list A.

Now let's break down each expression to help find their equivalent equations:

Expression 1: 6x+12
This expression can be simplified by factoring out the common factor 6.
So, 6x+12 = 6(x+2)
Therefore, the equivalent equation for the expression 6x+12 is 6(x+2).

Expression 2: 6+6x
Similarly, this expression can be simplified by factoring out the common factor 6.
So, 6+6x = 6(1+x)
Therefore, the equivalent equation for the expression 6+6x is 6(1+x).

Expression 3: 6(x-1)
This expression is already in its simplest form, and no further simplification is needed.
Therefore, the equivalent equation for the expression 6(x-1) remains the same, 6(x-1).

Now let's fill in the blanks accordingly:

The expression 6x+12 is equivalent to the expression 6(x+2).
The expression 6+6x is equivalent to the expression 6(1+x).
The expression 6(x-1) is equivalent to the expression 6(x-1).

I hope this explanation helps you understand how to solve and find the equivalent equations for expressions like these. If you have any further doubts or questions, feel free to ask!