Question

Solve the following equation. Be sure to check your proposed solution by substituting it for the variable in the given equation.
9 x minus 7 equals 5 x minus 59
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set is StartSet nothing EndSet .
  
​(Type an integer or a simplified​ fraction.)
B.
The solution set is StartSet x vertical line x is a real number EndSet.
C.
The solution set is empty set.

Answer 1

To solve the equation \( 9x - 7 = 5x - 59 \), we will isolate \( x \) on one side.

1. **Subtract \( 5x \) from both sides:**
\[
9x - 5x - 7 = -59
\]
This simplifies to:
\[
4x - 7 = -59
\]

2. **Add 7 to both sides:**
\[
4x - 7 + 7 = -59 + 7
\]
This simplifies to:
\[
4x = -52
\]

3. **Divide both sides by 4:**
\[
x = \frac{-52}{4} = -13
\]

Now, we have found a proposed solution \( x = -13 \).

Next, we will check this solution by substituting it back into the original equation.

**Substitute** \( x = -13 \) into the left side of the original equation:
\[
9(-13) - 7 = -117 - 7 = -124
\]

**Substitute** \( x = -13 \) into the right side of the original equation:
\[
5(-13) - 59 = -65 - 59 = -124
\]

Both sides are equal, confirming that \( x = -13 \) is indeed a solution.

Putting this all together, we can conclude that the solution set is:
\[
\text{The solution set is } \{ -13 \}.
\]

Thus, the final answer is:
**A. The solution set is \{ -13 \}**.