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solve and show clear working out and steps

Sure, let's solve each of these linear equations step-by-step.

### a. \(\frac{x}{4} + 1 = 3\)
1. Subtract 1 from both sides:
   \[
   \frac{x}{4} = 3 - 1
   \]
   \[
   \frac{x}{4} = 2
   \]
2. Multiply both sides by 4:
   \[
   x = 2 \times 4
   \]
   \[
   x = 8
   \]

### b. \(\frac{x}{3} - 2 = -1\)
1. Add 2 to both sides:
   \[
   \frac{x}{3} = -1 + 2
   \]
   \[
   \frac{x}{3} = 1
   \]
2. Multiply both sides by 3:
   \[
   x = 1 \times 3
   \]
   \[
   x = 3
   \]

### c. \(\frac{x}{8} = \frac{1}{2}\)
1. Multiply both sides by 8:
   \[
   x = \frac{1}{2} \times 8
   \]
   \[
   x = 4
   \]

### d. \(-\frac{x}{3} = 5\)
1. Multiply both sides by -3:
   \[
   x = 5 \times (-3)
   \]
   \[
   x = -15
   \]

### e. \(5 - \frac{x}{2} = -8\)
1. Subtract 5 from both sides:
   \[
   -\frac{x}{2} = -8 - 5
   \]
   \[
   -\frac{x}{2} = -13
   \]
2. Multiply both sides by -2:
   \[
   x = -13 \times (-2)
   \]
   \[
   x = 26
   \]

### f. \(4 - \frac{x}{6} = 11\)
1. Subtract 4 from both sides:
   \[
   -\frac{x}{6} = 11 - 4
   \]
   \[
   -\frac{x}{6} = 7
   \]
2. Multiply both sides by -6:
   \[
   x = 7 \times (-6)
   \]
   \[
   x = -42
   \]

Here are the solutions summarized:

- a. \( x = 8 \)
- b. \( x = 3 \)
- c. \( x = 4 \)
- d. \( x = -15 \)
- e. \( x = 26 \)
- f. \( x = -42 \)

Would you like further details on any of these steps or have any questions?

Here are five questions you might want to ask next:
1. How do you solve quadratic equations?
2. Can you explain how to solve a system of linear equations?
3. What are some methods to solve inequalities?
4. How do you find the slope of a line given two points?
5. Can you explain the process of factoring polynomials?

**Tip:** When solving equations, always perform the same operation on both sides to maintain equality.

Learn how to solve linear equations involving fractions with clear step-by-step solutions. This problem covers solving equations using multiplication and division properties, suitable for students in Grades 6-8.

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