https://file.aiquickdraw.com/mathbot/file/17260734638782ii66erk.jpg

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!

Simplify -3x + 4(2x - 5y) - 10y and solve several linear equations.

Learn how to simplify expressions like -3x + 4(2x - 5y) - 10y and solve linear equations. Step-by-step solutions cover the distributive property, simplification, and basic algebraic techniques. Suitable for Grades 7-9 students.

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