https://file.aiquickdraw.com/mathbot/file/1727998229936mr41wjws.pdf

It looks like your document contains algebra exercises focusing on solving equations, determining functions, and identifying the domain and range of sets of points.

Here’s a quick breakdown of the key problems:

1. **Solve the following equations**:
   - \( 4x + 5 = 2x - 3 \)
   - \(- (2x + 1) = 5 \)
   - \( 30 = 10x - 2x + 65 \)

2. **Functions, Domain, and Range**: You are asked to determine whether sets of coordinates represent functions and to list their domain (set of input values) and range (set of output values).

   Example: 
   - Set a: \( \{(9, 8), (7, 4), (-3, 9), (2, 8)\} \)
   - Set b: \( \{(-3, 4), (-7, -4), (-3, 2), (6, 8)\} \)

   You’ll also use the **Vertical Line Test** to identify if a graph represents a function.

3. **Write an equation** based on the statement:
   - "Eight less than three times a number is three."

4. **Solve and simplify more equations**, such as:
   - \( 5x + 4x - 5 - 2x + 3 - 7x \)

Would you like a detailed explanation of any specific problem? Here are some questions related to this topic to expand your understanding:

1. What is the process for determining if a relation is a function?
2. How can you apply the vertical line test to graphs?
3. Can a relation have repeating output values (range) and still be a function?
4. How do you simplify algebraic expressions with like terms?
5. What strategies can help you solve linear equations faster?

**Tip**: When checking if a set of coordinates represents a function, remember that for each input (x-value), there should be only one output (y-value).

Solve the following equations and analyze the coordinates to determine if they are functions. Additionally, simplify algebraic expressions and apply the vertical line test.

Learn how to solve algebraic equations, determine if coordinate sets are functions using the vertical line test, and simplify expressions. Includes step-by-step solutions for problems related to domain, range, and functions. Suitable for students in Grades 7-9.

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