2) Solve the following equations:
a.  -9x– 13 =-103 
b.  3/2 𝑛 − 8/3 = −29/12

Let's solve the given equations one by one.

### (a) \(-9x - 13 = -103\)

Step 1: Add 13 to both sides to isolate the term with \(x\).
\[
-9x = -103 + 13
\]
\[
-9x = -90
\]

Step 2: Divide both sides by \(-9\) to solve for \(x\).
\[
x = \frac{-90}{-9}
\]
\[
x = 10
\]

So, the solution to part (a) is \(x = 10\).

---

### (b) \(\frac{3}{2}n - \frac{8}{3} = \frac{-29}{12}\)

Step 1: Eliminate the fractions by finding the least common denominator (LCD), which is 12. Multiply the entire equation by 12:
\[
12 \times \left(\frac{3}{2}n\right) - 12 \times \left(\frac{8}{3}\right) = 12 \times \left(\frac{-29}{12}\right)
\]
\[
6 \cdot 3n - 4 \cdot 8 = -29
\]
\[
18n - 32 = -29
\]

Step 2: Add 32 to both sides.
\[
18n = -29 + 32
\]
\[
18n = 3
\]

Step 3: Divide both sides by 18 to solve for \(n\).
\[
n = \frac{3}{18}
\]
\[
n = \frac{1}{6}
\]

So, the solution to part (b) is \(n = \frac{1}{6}\).

---

### Final Answers:
- (a) \(x = 10\)
- (b) \(n = \frac{1}{6}\)

Do you want more details or have any questions?

Here are 5 related questions:
1. What happens when dividing both sides of an equation by a negative number?
2. How do you handle equations with multiple fractions?
3. What is the LCD and how is it useful in solving fractional equations?
4. Can equations always be solved by isolating variables in a single step?
5. How do you check if your solution to an equation is correct?

**Tip:** Always double-check your final answer by substituting it back into the original equation to verify it satisfies the equation.

2) Solve the following equations: a. -9x - 13 = -103 b. 3/2 𝑛 − 8/3 = −29/12

Learn how to solve the linear equation -9x - 13 = -103 and the fractional equation 3/2n - 8/3 = -29/12. This guide covers key algebraic concepts and step-by-step solutions suitable for students in Grades 6-8.

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