Answer:
(1) x + 7 = 18 -> YES
(2) x + 14 = 36 -> NO
(3) 2x + 14 = 36 -> YES
(4) 2x + 7 = 36 -> NO
(5) 2(x + 7) = 72 -> NO
(6) (2 times x) + (2 times 7) = 36 -> YES
Explanation:
(1) In this equation, what is being focused on is that in the initial equation, 2 is being multiplied by (x + 7). Therefore, in an attempt to isolate the x, you can divide by 2 in both sides! You want x to be the only term on one side of the equation, so moving the 2 to the other side is a great first step!
(2) In this equation, everything is the same, except the 2 is gone and the 7 magically turned into a 14. The missing 2 signals that someone divided by 2 on both sides, but this would result in the first equation, not this one. Also, the 7 magically becoming a 14 makes this a completely different equation.
(3) This represents a classic way of solving the equation: the Distrivurive Propert! Because 2 is being multiplied by an expression in parentheses, the 2 can be multiplied by each term inside the parentheses. 2(x) = 2x + 2(7) = 14, which nothing on the other side of the equation changes. This means that the Distributive Property has been used, which is a very good first step.
(4) This equation makes it look like the Distributive Property has been used by showing no change to the 36 and multiplying x by 2. However, 7 was left alone, and thus the Distributive Property was not completed and this is a half-attempt at a first step.
(5) In this equation, everything is the same in the initial equation, except the 36 has turned into a 72, which is 36(2). Anything done to one side of an equation must also be done to the other side, meaning that is 36 was multiplied by 2, 2(x +7) would have to be multiplied by 2, making an equation that looks like this: 4(x + 7) = 72. This is not the case, and either way multiplying by 2 is not a proper first step, so this is incorrect.
(6) This represents a more spread out version of the Distributive Property and illustrates the process that the Distributive Property represents. Therefore, this is a correct answer!
When it comes to answering problems like this, think about the way that you personally would solve this problem, and then try to come up with all of the alternative ways too. Figure out the first step of each of these methods and then compare them to the answer choices. If it does not match the first step of any of the methods that you tried out, investigate a little further to see if you missed a method, but most of the time that answer choice will be incorrect.
I hope this helped!!!