https://file.aiquickdraw.com/mathbot/file/1728557524141st3rbn7m.jpg

Let's go through the questions from the image.

### Part 1: True/False Statements
1. **Determine whether each of the following is true and circle your answer:**

   (a) \( 2x + 3 = 5 \) is an equation.  
   **Answer**: True. This is a linear equation in one variable \(x\).

   (b) \( 3y + 2 \) is an equation.  
   **Answer**: False. This is not an equation because it lacks an equals sign. It’s an expression.

   (c) If \(c = 8\), then \(3c = 38\).  
   **Answer**: False. If \( c = 8 \), then \( 3c = 3(8) = 24 \), not 38.

   (d) If \( a = \frac{4}{3} \), then \( 4 + a = 4a \).  
   **Answer**: False. Substituting \( a = \frac{4}{3} \), we get \( 4 + \frac{4}{3} \neq 4 \times \frac{4}{3} \).

   (e) \( x = 7 \) is the solution of the equation \( x + 2 = 5 \).  
   **Answer**: False. The solution to \( x + 2 = 5 \) is \( x = 3 \), not \( x = 7 \).

   (f) The equations \( 13 - d = 7 \) and \( \frac{d}{2} + 3 = 6 \) have the same solution.  
   **Answer**: True. Both equations have the solution \( d = 6 \).

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### Part 2: Matching Equations to Solutions
2. **Match the equations on the left with their solutions on the right:**

   (a) \( 9 - d = 2 \)  
   To solve:  
   \( d = 9 - 2 = 7 \)  
   **Answer**: (iv) 7

   (b) \( 7x = 21 \)  
   To solve:  
   \( x = \frac{21}{7} = 3 \)  
   **Answer**: (v) 3

   (c) \( c - 3 = 5 \)  
   To solve:  
   \( c = 5 + 3 = 8 \)  
   **Answer**: (i) 8

   (d) \( x + 4 = 8 \)  
   To solve:  
   \( x = 8 - 4 = 4 \)  
   **Answer**: (vi) 4

   (e) \( \frac{y}{2} = 3 \)  
   To solve:  
   \( y = 3 \times 2 = 6 \)  
   **Answer**: (iii) 6

   (f) \( 12 = 7a - 2 \)  
   To solve:  
   \( 7a = 12 + 2 = 14 \)  
   \( a = \frac{14}{7} = 2 \)  
   **Answer**: (ii) 2

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Let me know if you'd like more details on any part of this, or if you have questions!

Here are five related questions for practice:
1. What is the solution to the equation \( 2x + 7 = 15 \)?
2. How do you solve \( \frac{x}{4} + 2 = 6 \)?
3. What are the key differences between an expression and an equation?
4. Solve for \( y \) in \( y + 5 = 10 \).
5. How would you check if two equations have the same solution?

**Tip**: Always isolate the variable when solving linear equations by performing inverse operations like addition, subtraction, multiplication, or division.

1. Determine whether each of the following is true and circle your answer. 2. Match the equations on the left with their solutions on the right.

This problem focuses on determining whether given equations are valid and matching linear equations with their correct solutions. The exercise covers core algebraic concepts like solving linear equations, properties of equality, and solution equivalency. Suitable for Grades 6-8 students.

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