Question

A student solved the following problem.

3/5t + 7 = -8

3/5t = -15

t = -9

Which of the following statements is true?

The solution is wrong, because the -15 should be -1.
The solution is wrong, because the -15 should be 1.
The solution is wrong, because the -9 should be -25.
The solution is correct.

Answer 1

To verify the student's solution, let's start from the original equation and go through the steps to see if the solution is correct.

The equation given is:

\[
\frac{3}{5}t + 7 = -8
\]

1. First, we will isolate the term containing \( t \). We can do that by subtracting 7 from both sides:

\[
\frac{3}{5}t = -8 - 7
\]

This simplifies to:

\[
\frac{3}{5}t = -15
\]

2. Next, to solve for \( t \), we will multiply both sides by the reciprocal of \( \frac{3}{5} \), which is \( \frac{5}{3} \):

\[
t = -15 \cdot \frac{5}{3}
\]

Calculating this gives:

\[
t = -\frac{75}{3}
\]

\[
t = -25
\]

Now, let's compare the result we found for \( t \) with the solution provided by the student:

The student found \( t = -9 \), but our calculation shows \( t = -25 \).

Based on this analysis, the correct statement is:

**The solution is wrong, because the -9 should be -25.**