Math: b03adde3

ID: b03adde3

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

Comment: The fundamentals of algebra with a little embellishment.

Method 1: Anyone familiar with the equation of an inverse relationship between two unknowns, say x and y—y = 1/x—ought to be comfortable switching the two unknowns in a single step. This problem is no different, even though there is a binomial to consider rather than an unknown by itself.

u - 3 = 6/(t - 2)

t - 2 = 6/(u - 3)

t = [6/(u - 3)] + 2

t = [6/(u - 3)] + [2(u - 3)/(u - 3)]

t = (6 + 2u - 6)/(u - 3)

t = 2u/(u - 3)

The correct answer is (D).

Method 2: Probably the best way to use Desmos is to substitute x for u and y for t. Then, there are no sliders necessary, and you can plug in the answer choices directly until you find a graph that is identical to the first one.

Through answer choice (C), there is no winner, so (D) must be the answer, but it never hurts to check.

Here, Desmos has chosen to use the same red to highlight the same function. The correct answer is (D).

Method 3: A little number sense can go a long way with algebraic answer choices. Looking at the original function, for instance, you can plug in something easy like u = 4, forcing t = 8. Then, check the answer choices for equivalence.

A. (8) = 1/(4) X

B. (8) = (2(4) + 9)/(4) --> 8 = (8 + 9)/4 --> 8 = 17/4 X

C. (8) = 1/((4) - 3) --> 8 = 1/1 X

D. (8) = 2(4)/((4) - 3) --> 8 = 8/1 √

Once again, the correct answer is (D).