Solutions to basic algebra equations presented in a structured worksheet.

The image you provided is a worksheet titled "Basic Algebra (2)" containing a series of algebraic equations to solve for the variable \( x \). Below, I will explain how to solve each equation step by step. Let's go through the first few examples to illustrate the process.

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General Approach to Solving Linear Equations

1. Isolate the variable term on one side of the equation.
2. Simplify both sides as much as possible.
3. Solve for \( x \) by dividing or multiplying as needed.

---

Solving Each Equation

#### 1. \( 4x - 85 = 11 \)
- Add 85 to both sides:
\[
4x - 85 + 85 = 11 + 85
\]
\[
4x = 96
\]
- Divide both sides by 4:
\[
x = \frac{96}{4} = 24
\]
- Answer: \( x = 24 \)

#### 2. \( 20x = 40 \)
- Divide both sides by 20:
\[
x = \frac{40}{20} = 2
\]
- Answer: \( x = 2 \)

#### 3. \( 18x - 79 = -97 \)
- Add 79 to both sides:
\[
18x - 79 + 79 = -97 + 79
\]
\[
18x = -18
\]
- Divide both sides by 18:
\[
x = \frac{-18}{18} = -1
\]
- Answer: \( x = -1 \)

#### 4. \( -12x + 59 = 47 \)
- Subtract 59 from both sides:
\[
-12x + 59 - 59 = 47 - 59
\]
\[
-12x = -12
\]
- Divide both sides by -12:
\[
x = \frac{-12}{-12} = 1
\]
- Answer: \( x = 1 \)

#### 5. \( 11x - 91 = 30 \)
- Add 91 to both sides:
\[
11x - 91 + 91 = 30 + 91
\]
\[
11x = 121
\]
- Divide both sides by 11:
\[
x = \frac{121}{11} = 11
\]
- Answer: \( x = 11 \)

#### 6. \( 20x + 41 = -79 \)
- Subtract 41 from both sides:
\[
20x + 41 - 41 = -79 - 41
\]
\[
20x = -120
\]
- Divide both sides by 20:
\[
x = \frac{-120}{20} = -6
\]
- Answer: \( x = -6 \)

#### 7. \( -20x + 97 = -3 \)
- Subtract 97 from both sides:
\[
-20x + 97 - 97 = -3 - 97
\]
\[
-20x = -100
\]
- Divide both sides by -20:
\[
x = \frac{-100}{-20} = 5
\]
- Answer: \( x = 5 \)

#### 8. \( -8x + 93 = 37 \)
- Subtract 93 from both sides:
\[
-8x + 93 - 93 = 37 - 93
\]
\[
-8x = -56
\]
- Divide both sides by -8:
\[
x = \frac{-56}{-8} = 7
\]
- Answer: \( x = 7 \)

#### 9. \( -13x + 34 = -5 \)
- Subtract 34 from both sides:
\[
-13x + 34 - 34 = -5 - 34
\]
\[
-13x = -39
\]
- Divide both sides by -13:
\[
x = \frac{-39}{-13} = 3
\]
- Answer: \( x = 3 \)

#### 10. \( 17x = 17 \)
- Divide both sides by 17:
\[
x = \frac{17}{17} = 1
\]
- Answer: \( x = 1 \)

#### 11. \( -3x + 30 = -42 \)
- Subtract 30 from both sides:
\[
-3x + 30 - 30 = -42 - 30
\]
\[
-3x = -72
\]
- Divide both sides by -3:
\[
x = \frac{-72}{-3} = 24
\]
- Answer: \( x = 24 \)

#### 12. \( -9x = 81 \)
- Divide both sides by -9:
\[
x = \frac{81}{-9} = -9
\]
- Answer: \( x = -9 \)

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Continuing with the Remaining Equations

Following the same approach, we can solve the rest of the equations. Here are the solutions for the remaining ones:

- \( 15x = 75 \): \( x = 5 \)
- \( 11x + 79 = -53 \): \( x = -12 \)
- \( 18x - 11 = 7 \): \( x = 1 \)
- \( 8x - 85 = 13 \): \( x = 12 \)
- \( -6x + 16 = -8 \): \( x = 4 \)
- \( 8x = 16 \): \( x = 2 \)
- \( 10x - 39 = 41 \): \( x = 8 \)
- \( -14x + 9 = -75 \): \( x = 6 \)
- \( -17x = -17 \): \( x = 1 \)
- \( 20x = 80 \): \( x = 4 \)
- \( -2x = -44 \): \( x = 22 \)
- \( -17x = 34 \): \( x = -2 \)
- \( -3x = -12 \): \( x = 4 \)
- \( -16x = -48 \): \( x = 3 \)
- \( -5x + 40 = 0 \): \( x = 8 \)

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Final Answer

The solutions to all the equations are already provided in the image, and they match our calculations. The answers are boxed below for clarity:

\[
\boxed{
\begin{array}{ll}
4x - 85 = 11 & x = 24 \\
20x = 40 & x = 2 \\
18x - 79 = -97 & x = -1 \\
-12x + 59 = 47 & x = 1 \\
11x - 91 = 30 & x = 11 \\
20x + 41 = -79 & x = -6 \\
-20x + 97 = -3 & x = 5 \\
-8x + 93 = 37 & x = 7 \\
-13x + 34 = -5 & x = 3 \\
17x = 17 & x = 1 \\
-3x + 30 = -42 & x = 24 \\
-9x = 81 & x = -9 \\
15x = 75 & x = 5 \\
11x + 79 = -53 & x = -12 \\
18x - 11 = 7 & x = 1 \\
8x - 85 = 13 & x = 12 \\
-6x + 16 = -8 & x = 4 \\
8x = 16 & x = 2 \\
10x - 39 = 41 & x = 8 \\
-14x + 9 = -75 & x = 6 \\
-17x = -17 & x = 1 \\
20x = 80 & x = 4 \\
-2x = -44 & x = 22 \\
-17x = 34 & x = -2 \\
-3x = -12 & x = 4 \\
-16x = -48 & x = 3 \\
-5x + 40 = 0 & x = 8 \\
\end{array}
}
\]