− 
2
1
​
 =
− 
8
7
​
 − 
4
1
​
 z

The given equation is:

\[
-\frac{2}{1} = -\frac{8}{7} - \frac{4}{1}z
\]

First, simplify \(-\frac{2}{1}\) and \(-\frac{4}{1}\) to \(-2\) and \(-4\) respectively:

\[
-2 = -\frac{8}{7} - 4z
\]

Next, add \(\frac{8}{7}\) to both sides to isolate the term with \(z\):

\[
-2 + \frac{8}{7} = -4z
\]

Convert \(-2\) to a fraction with a denominator of 7:

\[
-\frac{14}{7} + \frac{8}{7} = -4z
\]

Combine the fractions:

\[
-\frac{6}{7} = -4z
\]

Now, divide both sides by \(-4\) to solve for \(z\):

\[
z = \frac{\frac{6}{7}}{4}
\]

Simplify the expression:

\[
z = \frac{6}{28} = \frac{3}{14}
\]

Thus, the solution is:

\[
z = \frac{3}{14}
\]

Would you like more details or have any questions?

Here are five related questions to expand on this concept:
1. How would the solution change if the equation was \(-\frac{2}{1} = -\frac{8}{7} + \frac{4}{1}z\)?
2. Can you solve for \(z\) if the equation was \(2 = -\frac{8}{7} - 4z\)?
3. What happens if the equation was multiplied by 7 on both sides?
4. How would you solve the equation if the term with \(z\) had a different denominator?
5. What are the implications if \(z\) is required to be a whole number?

**Tip:** When solving equations, always ensure all terms are simplified first, and fractions have a common denominator if necessary.

Explore how to solve the linear equation -2 = -8/7 - 4z with a detailed step-by-step solution. This problem covers key algebraic concepts, including fraction simplification and isolating variables. Suitable for students in Grades 8-10.

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