6 times the reciprocal of a number equals 3 times the reciprocal of 7 .

This is an algebraic expression. Let's take it in parts:

The phrase a number means an arbitrary variable, let's call it x.
x

The reciprocal of a number x means we divide 1 over x:
1/x

6 times the reciprocal means we multiply 6 by 1/x:
6/x

The reciprocal of 7 means we divide 1/7
1/7

3 times the reciprocal means we multiply 1/7 by 3:
3/7

Now, the phrase equals mean an equation, so we set 6/x = 3/7
6/x = 3/7 <-- This is our algebraic expression

If the problem asks you to solve for x, then we type this proportion in our search engine and get:
x = 14

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