Final answer:
To find terms to add so that x = 2 is the solution, we simplify the left side of the equation -2(4x - 1) + 15x to get 7x + 2. Adding +13 or -9 to the left side results in an equation where x = 2 is a solution.
Step-by-step explanation:
The question requires us to find terms to add on the right side of the equation so that x = 2 is the solution for the equation -2(4x - 1) + 15x. To find the right terms, we first simplify the left side of the equation and then determine what to add to both sides to maintain the equality.
Let's simplify the left side:
-2(4x - 1) + 15x = -8x + 2 + 15x
Now, we combine like terms:
-8x + 15x = 7x
So, the equation becomes:
7x + 2 = ?
To make x = 2 a solution, the right side of the equation must equal the left side when x = 2. So we find:
7(2) + 2 = 14 + 2 = 16
Therefore, the right side of the equation should be 16 in order for x = 2 to be the solution. Among the given options, none directly equals 16. However, we can create an expression that when added to the left side results in 16. For instance, we could add +13 to the left side, since 7x + 2 +13 becomes 7x + 15, which equals 16 when x = 2. As such, Option 1: +13 is a correct term to add. Similarly, we could also add -9 to 7x, to get 7x - 7, which would also equal 16 when x = 2; hence, Option 4: -9 is another possible term.