1958 AMC 12 Problem 34

Question

The numerator of a fraction is

6x+1,

the denominator is

7-4x,

and

x

can have any value between

-2

and

2,

both included. The values of

x

for which the numerator is greater than the denominator are:

\dfrac35\lt x\le2

\dfrac35\le x\le2

0\lt x\le2

0\le x\le2

-2\le x\le2

Compare the numerator and denominator directly by solving

6x+1\gt7-4x

Intersect the resulting inequality with the given interval

[-2,2]

The required comparison gives

6x+1\gt7-4x,

so

10x\gt6

and

x\gt\frac{3}{5}.

Intersecting this with

-2\le x\le2

gives

\frac35\lt x\le2.

Thus, the correct answer is A.

Problem 34 in other years