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June 24, 2010

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GMAT Math Tip: U-Substitution

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Finding ways to turn complex problems into simple ones is a valuable skill when taking the GMAT.  U-substitution is a technique that can help accomplish this.  It will save you time and decrease the likelihood that you will make a mistake.  In the following video and example, we examine u-substitution in more detail.

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Below is a GMAT math problem on which you can apply the u-substitution technique.

If (3x + 1)2 – 14(3x+1) + 49 = 0 then x =

(A) -7
(B) -3
(C) 2
(D) 6
(E) 7

The first step is identifying the common element (3x + 1 in this example.)  Then rewrite the equation substituting u for 3x + 1:

Let u = 3x + 1
u2 – 14u + 49 = 0

Factor the equation, and solve for u:

(u – 7)(u – 7) = 0
u – 7 = 0
u = 7

Now that you have solved for u, solve for x:

3x + 1 = u
3x + 1 = 7
3x = 6
x = 2

The answer is C, 2.

Today’s article was brought to you by Beat The GMAT.  To try more practice questions with similar video explanations, check out Smart GMAT Practice.

Last updated on November 24, 2016.

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