Question
Which statement corresponds with the equation 34n−19=−1
(1 point)
Responses
The sum of three fourths of a number and nineteen is negative one.
The sum of three fourths of a number and nineteen is negative one.
The difference between nineteen and three fourths of a number is negative one.
The difference between nineteen and three fourths of a number is negative one.
Three fourths of a number decreased by nineteen is negative one.
Three fourths of a number decreased by nineteen is negative one.
Three fourths of nineteen decreased by a number is negative one.
(1 point)
Responses
The sum of three fourths of a number and nineteen is negative one.
The sum of three fourths of a number and nineteen is negative one.
The difference between nineteen and three fourths of a number is negative one.
The difference between nineteen and three fourths of a number is negative one.
Three fourths of a number decreased by nineteen is negative one.
Three fourths of a number decreased by nineteen is negative one.
Three fourths of nineteen decreased by a number is negative one.
Answers
GPT-4o mini
To analyze the equation \(34n - 19 = -1\), let's first isolate the term involving \(n\).
1. Add 19 to both sides:
\[
34n - 19 + 19 = -1 + 19
\]
Simplifying gives:
\[
34n = 18
\]
2. Now, let's divide both sides by 34 to solve for \(n\):
\[
n = \frac{18}{34} = \frac{9}{17}
\]
Now, to interpret the original equation \(34n - 19 = -1\) in terms of the provided responses, we break down \(34n - 19\):
- \(34n\) represents "three fourths of a number, multiplied by a factor of 34."
The equation can be interpreted in context:
- The left side (\(34n - 19\)) means you start with "three fourths of a number (34n) and then decrease it by nineteen."
Now let's evaluate the given responses:
1. **The sum of three fourths of a number and nineteen is negative one.** — This does not match the original equation.
2. **The difference between nineteen and three fourths of a number is negative one.** — This can be rearranged to:
\[
19 - (34n) = -1 \quad \Rightarrow \quad 19 + 1 = 34n \quad \Rightarrow \quad 20 = 34n
\]
— This does not match.
3. **Three fourths of a number decreased by nineteen is negative one.** — This statement matches the left side expression and can be expressed as:
\[
34n - 19 = -1
\]
— This is correct.
4. **Three fourths of nineteen decreased by a number is negative one.** — This does not align with the equation structure.
Therefore, the statement that corresponds with the equation \(34n - 19 = -1\) is:
**Three fourths of a number decreased by nineteen is negative one.**
1. Add 19 to both sides:
\[
34n - 19 + 19 = -1 + 19
\]
Simplifying gives:
\[
34n = 18
\]
2. Now, let's divide both sides by 34 to solve for \(n\):
\[
n = \frac{18}{34} = \frac{9}{17}
\]
Now, to interpret the original equation \(34n - 19 = -1\) in terms of the provided responses, we break down \(34n - 19\):
- \(34n\) represents "three fourths of a number, multiplied by a factor of 34."
The equation can be interpreted in context:
- The left side (\(34n - 19\)) means you start with "three fourths of a number (34n) and then decrease it by nineteen."
Now let's evaluate the given responses:
1. **The sum of three fourths of a number and nineteen is negative one.** — This does not match the original equation.
2. **The difference between nineteen and three fourths of a number is negative one.** — This can be rearranged to:
\[
19 - (34n) = -1 \quad \Rightarrow \quad 19 + 1 = 34n \quad \Rightarrow \quad 20 = 34n
\]
— This does not match.
3. **Three fourths of a number decreased by nineteen is negative one.** — This statement matches the left side expression and can be expressed as:
\[
34n - 19 = -1
\]
— This is correct.
4. **Three fourths of nineteen decreased by a number is negative one.** — This does not align with the equation structure.
Therefore, the statement that corresponds with the equation \(34n - 19 = -1\) is:
**Three fourths of a number decreased by nineteen is negative one.**