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 =
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.