Plugging In
When faced with complicated algebraic expressions, test takers can get confused
or flustered. Although simple problems should be solved algebraically, more
complicated problems can be solved in another way. Instead of working through
the problem algebraically, consider substituting numbers for variables.
Choose numbers that are easy to work with, such as 1, 2, or 10. Also try a
negative number such as –1 or –2. Zero is useful, too.
Example:
Last year, a town had a population of 2,000 + x. If the population
increased by 25 people this year, which of the following expressions
represents this year’s population?
A) 2,000 + 25x
B) 2,025 + x
C) 5,000 + 25x
D) 5,250 + xWhile this can be solved using pure algebra, substituting the number 1 for x is
an easy alternative. By doing this, the population was 2001 and then increased
by 25, becoming 2,026. By substituting 1 for x in the answer choices, you find
that B is correct.
More complicated example:
4 x + 4x + 4x + 4x =
A) 4(x + 1)
B) 4(x + 2)
C) 4(x + 4)
D) 4(x(^4) )
This problem can be solved algebraically, by saying that 4x+ 4x+ 4x+ 4x = 4 ×
4 x = 4(x + 1). If, however, you get stuck or have a difficult time following this
method, you can plug in a number for x instead. By saying that x = 2, 4^2 + 4^2 + 4^2
- 4^2 = 64 = 4^3 . Therefore, the answer is 4(x + 1) or choice A.