Math: 771bd0ca

ID: 771bd0ca 

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

Comment: Sometimes it pays to get inventive to do less work.

Method 1: It can be tempting to distribute and solve for the unknown whenever you see such a straightforward algebra problem, and that is one method of tackling the question. However, you can alternatively use a shorthand to sidestep all the extra steps and still arrive at an accurate conclusion. In problems like the one at hand, I often advise advanced students to create a variable m to stand in for a lengthier binomial.

Let m = t + 3

5(m) - 7(m) = 38

-2m = 38

m = -19

(t + 3) = -19

t = -22

The answer is -22.

The benefits of this substitution method are apparent when you consider a more complex example. If, instead of t + 3, the part that concerned the substitution was something like t^2 - 3t + 5, it might be much simpler and efficient to swap out the quadratic for a single unknown such as m.

Method 2: This must be one of the simplest calculator questions of this difficulty (Hard). You can use Desmos to graph the line and highlight the solution.

Since the question asks for the value of t, or x in the equation above, you can simply type what you see: the answer is -22.

Method 3: If the above two methods elude you in the moment, you could brute force your way through the algebra without too much difficulty.

5(t + 3) - 7(t + 3) = 38

5t + 15 - 7t - 21 = 38

-2t - 6 = 38

-2t = 44

t = -22

The answer is -22 all the same.