https://file.aiquickdraw.com/mathbot/file/1726014308020idzysnk9.jpg

The image contains several sections of algebraic equations to solve. Here is a breakdown of each section:

### Section A
These are linear equations that involve fractions and basic algebraic operations. Let's solve the first few:

1. \(\frac{2x + 5}{3} = 11\)

Multiply both sides by 3:
\[
2x + 5 = 33
\]

Subtract 5 from both sides:
\[
2x = 28
\]

Divide by 2:
\[
x = 14
\]

2. \(\frac{8 - 3x}{2} = 5\)

Multiply both sides by 2:
\[
8 - 3x = 10
\]

Subtract 8 from both sides:
\[
-3x = 2
\]

Divide by -3:
\[
x = -\frac{2}{3}
\]

### Section B
This section contains linear equations with more complex terms, often involving parentheses.

1. \(4(2x - 3) = 8(2x + 5)\)

Expand both sides:
\[
8x - 12 = 16x + 40
\]

Combine like terms:
\[
-12 - 40 = 16x - 8x
\]

\[
-52 = 8x
\]

\[
x = -\frac{52}{8} = -\frac{13}{2}
\]

### Section C
These problems are more advanced, involving rational expressions. For example:

1. \(\frac{5x - 2}{3} = \frac{4x + 1}{2}\)

Cross-multiply:
\[
2(5x - 2) = 3(4x + 1)
\]

Expand:
\[
10x - 4 = 12x + 3
\]

Combine like terms:
\[
10x - 12x = 3 + 4
\]

\[
-2x = 7
\]

\[
x = -\frac{7}{2}
\]

Would you like me to continue solving specific problems, or explain a particular step in more detail? Feel free to let me know!

### Related Questions:
1. How do you solve linear equations with fractions?
2. What is the process for solving systems of equations with two variables?
3. How do you simplify algebraic expressions involving parentheses?
4. What are common mistakes when solving equations involving fractions?
5. How can rational expressions be solved efficiently?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Solve the algebraic equations in the image provided.

This page offers detailed solutions to a variety of algebraic equations covering linear equations, rational expressions, and complex expressions involving parentheses. These problems are designed to enhance understanding of fundamental algebraic principles suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation