Math: aee9fd2d

ID: aee9fd2d 

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: A little substitution can go a long way.

Method 1: Notice that the equation and the question both pertain to the quantity x + 6, not x by itself. It may help to reframe this binomial as, say, m so that you can more easily work out the arithmetic, without the distraction of an extra term.

Let m = x + 6

(m)/3 = (m)/13

13m = 3m

10m = 0

m = 0

Since 0 lies between -2 and 2, the correct answer is (B). This might even be a question you could answer without writing anything down, or by jotting down the start of the substitution only. As long as you know the answer, and you make sure you answer the question being asked, it does not matter if you work everything out.

Method 2: Plug in the equation to Desmos. 

The graph shows the solution for x, not x + 6. If you substitute -6 for x, you get (-6) + 6 = 0, and the correct answer is (B). However, I imagine a fair number of students would choose (A) without thinking about just what the question is asking. If you have organizational issues that are costing you points, you might consider a substitution strategy such as the one outlined above, in method 1. For instance, let x represent the binomial x + 6.

This second graph shows the proper solution for the quantity x + 6. Again, the correct answer must be (B).

Method 3: The long way is to multiply everything out, solve for x, then remember to answer the question. For the record, I would not recommend this method, although it is serviceable. Start by cross-multiplying.

13(x + 6) = 3(x + 6)

13x + 78 = 3x + 18

10x = -60

x = -6

x + 6 = (-6) + 6 = 0

The correct answer is (B).