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The image contains a list of linear equations in one variable, which are to be solved. Let's go through a few of them step-by-step:

### Equation 01:
\[ 2x - 34 = -20 \]

#### Step-by-step solution:
1. Add 34 to both sides to isolate the term with \(x\):
   \[
   2x = -20 + 34
   \]
   \[
   2x = 14
   \]
2. Divide both sides by 2:
   \[
   x = \frac{14}{2} = 7
   \]

### Equation 03:
\[ 4x + 3 = 3x + 5 \]

#### Step-by-step solution:
1. Subtract \(3x\) from both sides:
   \[
   4x - 3x + 3 = 5
   \]
   \[
   x + 3 = 5
   \]
2. Subtract 3 from both sides:
   \[
   x = 5 - 3
   \]
   \[
   x = 2
   \]

### Equation 05:
\[ x - 8 = 2x - 11 \]

#### Step-by-step solution:
1. Subtract \(x\) from both sides:
   \[
   -8 = x - 11
   \]
2. Add 11 to both sides:
   \[
   -8 + 11 = x
   \]
   \[
   3 = x
   \]

### Equation 07:
\[ 6x + 6 = 4 + 8x \]

#### Step-by-step solution:
1. Subtract \(6x\) from both sides:
   \[
   6 = 4 + 2x
   \]
2. Subtract 4 from both sides:
   \[
   2 = 2x
   \]
3. Divide both sides by 2:
   \[
   x = 1
   \]

### Equation 09:
\[ 2x + 1 = 3x \]

#### Step-by-step solution:
1. Subtract \(2x\) from both sides:
   \[
   1 = x
   \]

Would you like me to solve more of these equations or go into more details for the steps provided?

Here are 5 relative questions to further expand your understanding:
1. How do you solve equations with variables on both sides?
2. What is the process of transposing terms in an equation?
3. Can an equation have more than one solution?
4. How do you simplify terms in an equation before solving?
5. What happens if an equation leads to a false statement, like \( 0 = 1 \)?

**Tip:** When solving equations, always aim to isolate the variable on one side by performing inverse operations on both sides of the equation.

Solve the given list of linear equations in one variable.

Learn how to solve linear equations step-by-step with examples such as 2x - 34 = -20 and 4x + 3 = 3x + 5. This tutorial covers the core concepts of isolating variables, transposing terms, and applying inverse operations.

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