Cracking The SAT Premium

(D). If one of them does not, that one is the extraneous solution.

t   =   0 t =   5

    =   0   −   2   =   5   −   2

    =   −2  =   3

2   =   −2 3    =   3

Since the equation is false when t = 0, then 0 is the extraneous solution. The correct answer is (A).

Solving for Expressions

Some SAT algebra problems ask you to find the value of an expression rather than the value of a variable.
In most cases, you can find the value of the expression without finding the value of the variable.

5.If    4x  +   2   =   4,  what    is  the value   4x  −   6   ?

A) −6

B) −4

C) 4

D) 8

Math    Class   Solution:

In  math    class,  you would

find    the value   of  x   and

then    plug    that    value   into

the provided    expression.

So, subtract    2   from    both

sides   to  find    that    4x  =   2.

Then    divide  both    sides   by

4   to  find    that    x   =    .  Then,

4 x −   6   =   4       –6  =   –4.

So, the answer  is  (B).

Here’s How to Crack It

Since you’re being asked for the value of an expression (4x − 6) rather than the value of x, you correctly
suspect that there might be a shortcut. So, you look for a way to turn 4x + 2 into 4x − 6 and realize that
subtracting 8 from both sides of the equation will do just that.

So, you just do (4x + 2) − 8 = 4 − 8 = −4 and you’ve got (B).

The Princeton Review solution will save you time—provided that you see it quickly. So, while you
practice, you should train yourself to look for these sorts of direct solutions whenever you are asked to
solve for the value of an expression.