Source: Revised GRE PDF 1st Ed. Section 6: Math; #15

2

# If 1/2m + 1/2m = 1/2x

if 1/2m+1/2m=1/2x, then x expressed in terms of m is

### 2 Explanations

1

nicholas osemeke

1/2^m + 1/2^m = 1/2^x;

i solved this algebraically; ==> 1+1/(2^m) = 2^x
==> 2/2^m=1/2^x===cross multiply; m=x+1; x=m-1

May 24, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Nicholas :)

While Chris explains how to solve this problem by plugging in numbers, it is possible to solve the problem algebraically. You're correct that we can add the two terms on the left side, which leads us to

2/2^m = 1/2^x

However, at this point, we cannot simply cross multiply, as that would lead us to

2*2^x = 2^m

Instead, it's better to rewrite the left side, recognizing that we are dividing two exponents with the same base of 2:

2/2^m = 2^1/2^m = 2^(1-m)

Likewise, the left side can be rewritten as

2^(-x)

2^(1-m) = 2^(-x)

From here, we have exponents with the same base on the two sides of the equation and can compare the exponents to solve for x:

1-m = -x
m-1 = x

As you can see, we can solve this question algebraically, but the steps are somewhat involved and plugging in may be the better strategy for this problem. :)

2 Chris Lele, Magoosh Tutor

Oct 4, 2012 • Comment