Let's break down and solve each of the problems one by one from the image you've uploaded.

1) Simplify the expression:

$-3x + 4(2x - 5y) - 10y$

First, distribute the $4$ inside the parentheses: $= -3x + 4 \cdot 2x - 4 \cdot 5y - 10y$ $= -3x + 8x - 20y - 10y$

Now, combine like terms: $= (-3x + 8x) + (-20y - 10y)$ $= 5x - 30y$

So, the simplified expression is: $\boxed{5x - 30y}$

2) Solve the equation:

$4x - 3x + 2 = 18$

First, simplify the left side: $(4x - 3x) + 2 = 18$ $x + 2 = 18$

Now, subtract 2 from both sides: $x = 18 - 2$ $x = 16$

So, the solution is: $\boxed{x = 16}$

3) Solve the equation:

$\frac{4}{x} = 8$

To eliminate the fraction, multiply both sides by $x$: $4 = 8x$

Now, solve for $x$ by dividing both sides by 8: $x = \frac{4}{8}$ $x = \frac{1}{2}$

So, the solution is: $\boxed{x = \frac{1}{2}}$

4) Solve the equation:

$-7x = 35$

Divide both sides by $-7$: $x = \frac{35}{-7}$ $x = -5$

So, the solution is: $\boxed{x = -5}$

5) Solve the equation:

$\frac{x}{8} = 4$

Multiply both sides by 8: $x = 4 \cdot 8$ $x = 32$

So, the solution is: $\boxed{x = 32}$

Let me know if you need any details on these solutions!

Here are 5 related questions:

1. How do you apply the distributive property in algebra?
2. What are the steps to solve a linear equation?
3. How do you simplify expressions involving variables?
4. How do you solve an equation with fractions?
5. What are some methods for checking your solution in algebra?

Tip: Always combine like terms and apply the distributive property carefully to avoid errors when simplifying expressions!