SAT Math: Algebra

Symbol Problems

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A. -16
B. -4
C. -2
D. -1
E. -3/4

Knowsys Method

Read the problem carefully.  If you have never seen this problem type before, it might look strange to you.  Don't worry, though.  We will show you just how simple these problems are!

Identify the bottom line. c = ?

Assess your options.  At Knowsys, we call these problems "symbol problems" because they use non-mathematical symbols like stars, hearts, smiley faces, etc.  To solve a symbol problem, all you have to do is plug in the information given to you.  Use the following steps to ace these problems on the SAT. 

1. Write out the symbol problem defined in the question.  For instance,

&a = a + 2

2. Directly below that, write out the new version of the symbol problem, aligning the symbol in the original with the symbol in the new version.

&a = a + 2

&b =

&7 =

3. Substitute the variable(s) or number(s) in the new version for the variables in the original. 

&a = a + 2

&b = b + 2

&7 = 7 + 2 = 9

Attack the problem.  Let's apply those steps to the symbol problem above.  First, write out the original symbol problem defined in the question.

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You will have to deal with the right and left sides of the new version of the symbol problem separately.  Start with the right side.  Write that part out below the original, and substitute the variables into the original. 

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Now, repeat the same step with the left side. 

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Use FOIL, distribute the -2, and then combine like terms.

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Now, set the solutions you have found for each side equal to each other and solve for c.

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Loop back.  Check to make sure that you have solved for the bottom line.

The correct answer is D.

This is a hard level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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