The given equation is:

\[
\frac{-7}{1} = \frac{-7}{2} + \frac{43}{c}
\]

To solve for \(c\), let's go step by step:

1. Simplify the left-hand side:

\[
\frac{-7}{1} = -7
\]

Now the equation becomes:

\[
-7 = \frac{-7}{2} + \frac{43}{c}
\]

2. Isolate the term \(\frac{43}{c}\) by subtracting \(\frac{-7}{2}\) from both sides:

\[
-7 - \frac{-7}{2} = \frac{43}{c}
\]

3. Simplify the left-hand side. To subtract fractions, convert \(-7\) to a fraction with the same denominator:

\[
-7 = \frac{-14}{2}
\]

Now subtract:

\[
\frac{-14}{2} - \frac{-7}{2} = \frac{-14 + 7}{2} = \frac{-7}{2}
\]

So the equation is:

\[
\frac{-7}{2} = \frac{43}{c}
\]

4. Cross-multiply to solve for \(c\):

\[
-7c = 2 \times 43
\]

\[
-7c = 86
\]

5. Finally, solve for \(c\) by dividing both sides by \(-7\):

\[
c = \frac{86}{-7} = -\frac{86}{7}
\]

Thus, \(c = -\frac{86}{7}\).

---

Would you like more details on any step? Here are some related questions:

1. How do you simplify equations with fractions?
2. What are the properties of negative numbers in equations?
3. How do you handle cross-multiplication with fractions?
4. What is the significance of isolating variables in an equation?
5. Can you always cross-multiply when solving equations like this?

**Tip:** Always check your solution by substituting the variable back into the original equation!

Learn how to solve the equation -7/1 = -7/2 + 43/c with step-by-step explanations. This problem involves key algebraic concepts such as cross-multiplication, isolating variables, and handling fractions. Ideal for students in Grades 8-10.

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