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GMAT Quant Strategy: U-Substitution

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.

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.

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