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Some of the most challenging Problem Solving questions you encounter
will be algebraic in nature. Because algebra deals with variable numbers
and quantities, algebra questions are more abstract than arithmetic problems,
and abstract problems are often more complex problems. In the Problem
Solving Basics Workshop, we learned two strategies that make algebra problems
more manageable by making them resemble arithmetic problems - Picking
Numbers and Back solving.
Advanced algebra problems are also vulnerable to these backdoor strategies,
but a strong grasp of algebra will often provide a faster means of solving
the toughest questions. At other times, algebra will be necessary
to solve these types of problems. The key is to develop proficiency in
all three approaches so that you have a range of problem-solving tools
at your disposal, and to be able to identify the best approach for any
given algebra question.
Let's review a few points on identifying the best approach for a given
question, and then we'll move on to some examples:
Backsolving:
Any question that has numbers as answer choices is a possible candidate
for Backsolving. Beyond this, consider Backsolving on algebra questions
with text-based question stems. Word problems, for example, require English-to-math
translation skills when solved via textbook methods. If you are not comfortable
with algebra, or if you are short on time, Backsolving is often an option
on such questions.
Picking Numbers: Any question that has variables in the answer
choices is a possible candidate for Picking Numbers. In particular, try
using this strategy on algebra problems that contain multiple variables
or that include complex, unfamiliar algebraic expressions. Solving algebraically
in such cases often requires lots of abstract calculation, or the use
of a key algebraic step that may not be easy to identify.
Algebra:
Certain questions, in particular those that ask us to solve for
multiple variable expressions or complex amounts, must be solved algebraically.
Beyond this, using algebra can be faster than alternate methods if you
are comfortable manipulating expressions and variables, and translating
text to equation form .
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