Question

Which statement corresponds with the equation 3/4n - 19 = -1
A. Three fourths of nineteen decreased by a number is negative one.
B. The difference between nineteen and three fourths of a number is negative one.
C. The sum of three fourths of a number and nineteen is negative one.
D. Three fourths of a number decreased by nineteen is negative one.

Answer 1

To analyze the equation \( \frac{3}{4}n - 19 = -1 \) and find the corresponding statement, we can break it down:

1. The term \( \frac{3}{4}n \) refers to three fourths of a number \( n \).
2. The phrase "decreased by" indicates a subtraction.
3. The equation ends with the value of \(-1\).

Now let's match this with the answer choices:

A. "Three fourths of nineteen decreased by a number is negative one."
- This is incorrect because it suggests "three fourths of nineteen" instead of "three fourths of a number".

B. "The difference between nineteen and three fourths of a number is negative one."
- This implies \( 19 - \frac{3}{4}n = -1 \), which does not match our equation.

C. "The sum of three fourths of a number and nineteen is negative one."
- This refers to an addition, which is incorrect since the equation involves subtraction.

D. "Three fourths of a number decreased by nineteen is negative one."
- This correctly translates to the equation: \( \frac{3}{4}n - 19 = -1 \).

Thus, the correct answer is:

**D. Three fourths of a number decreased by nineteen is negative one.**