Solve for z*z*.

start fraction, 11, divided by, 12, end fraction, z, plus, 6, equals, 83

1211​*z*+6=

83

We are given the equation:

\[
\frac{11}{12}z + 6 = 83
\]

To solve for \( z \), follow these steps:

1. **Subtract 6 from both sides** to isolate the term with \( z \) on the left-hand side:
   \[
   \frac{11}{12}z = 83 - 6
   \]
   \[
   \frac{11}{12}z = 77
   \]

2. **Multiply both sides by 12** to eliminate the fraction:
   \[
   11z = 77 \times 12
   \]
   \[
   11z = 924
   \]

3. **Divide both sides by 11** to solve for \( z \):
   \[
   z = \frac{924}{11}
   \]
   \[
   z = 84
   \]

So, \( z = 84 \).

Let me know if you'd like further clarification!

Here are 5 related questions to explore this topic further:

1. How would the solution change if the constant 6 were replaced by another number?
2. What happens if the fraction is on the right side of the equation?
3. How can you solve an equation if the variable appears on both sides?
4. How do you solve an equation with fractions in more than one term?
5. How does multiplying or dividing by a negative number affect an equation?

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

Learn how to solve the linear equation (11/12)z + 6 = 83 with a detailed step-by-step solution. This problem involves key algebraic concepts, including isolating variables and eliminating fractions. Suitable for students in Grades 6-8.

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