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.