Which expression is equivalent to x/19 - 7/2?

• A. (2x - 133)/38
• B. (2x)/38 - 133/2
• C. (x - 7)/19
• D. (2x - 7)/38

Answer: (A)

Combining fractions by using a common denominator. To rewrite x/19 − 7/2 with a shared bottom, use 38 as the common denominator. x/19 becomes 2x/38, since multiplying numerator and denominator by 2 gives (2x)/38. 7/2 becomes 133/38, since multiplying numerator and denominator by 19 gives (133)/38. Subtracting the two with this common denominator yields (2x − 133)/38. This single-fraction form preserves the exact value of the original expression, matching the difference of the two terms.

Why the other forms don’t fit: keeping two fractions with different denominators isn’t a single combined expression, so it isn’t equivalent in simplified form. Replacing 7/2 with 7/19 would subtract a different amount, and using 7/38 would subtract an even smaller amount, both changing the value from the original.