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The image contains two equations that are meant to be solved using a "statement-reason" table approach. The equations are:

1. \( \frac{4x + 10}{4} = 2 \)
2. \( 5(x - 2) = 15 - (x - 5) \)

The structure suggests we will fill in the steps of solving these equations, with explanations ("reasons") for each algebraic step.

### Let's solve these step by step:

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**For Equation 1: \( \frac{4x + 10}{4} = 2 \)**

1. **Statement:** \( \frac{4x + 10}{4} = 2 \)
   **Reason:** Given equation.
   
2. **Statement:** \( 4x + 10 = 8 \)
   **Reason:** Multiply both sides by 4 to eliminate the denominator.

3. **Statement:** \( 4x = 8 - 10 \)
   **Reason:** Subtract 10 from both sides.

4. **Statement:** \( 4x = -2 \)
   **Reason:** Simplify the right side.

5. **Statement:** \( x = \frac{-2}{4} \)
   **Reason:** Divide both sides by 4.

6. **Statement:** \( x = -\frac{1}{2} \)
   **Reason:** Simplify the fraction.

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**For Equation 2: \( 5(x - 2) = 15 - (x - 5) \)**

1. **Statement:** \( 5(x - 2) = 15 - (x - 5) \)
   **Reason:** Given equation.

2. **Statement:** \( 5x - 10 = 15 - (x - 5) \)
   **Reason:** Distribute the 5 on the left-hand side.

3. **Statement:** \( 5x - 10 = 15 - x + 5 \)
   **Reason:** Distribute the negative sign on the right-hand side.

4. **Statement:** \( 5x - 10 = 20 - x \)
   **Reason:** Simplify the right-hand side.

5. **Statement:** \( 5x + x = 20 + 10 \)
   **Reason:** Add \(x\) to both sides and add 10 to both sides.

6. **Statement:** \( 6x = 30 \)
   **Reason:** Simplify both sides.

7. **Statement:** \( x = \frac{30}{6} \)
   **Reason:** Divide both sides by 6.

8. **Statement:** \( x = 5 \)
   **Reason:** Simplify the fraction.

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Would you like further clarification or details on these steps? Here are 5 related questions for practice:

1. How can you verify the solution for \( x = -\frac{1}{2} \) in the first equation?
2. Why is it important to distribute the negative sign in the second equation?
3. What method is used to clear fractions in the first equation?
4. What is the next step if an equation includes variables on both sides?
5. How can you check if your solution satisfies the original equation?

**Tip:** Always simplify both sides of the equation as much as possible before isolating the variable to make solving easier.

Solve the equations: 1. (4x + 10) / 4 = 2, 2. 5(x - 2) = 15 - (x - 5)

Learn how to solve the linear equations (4x + 10)/4 = 2 and 5(x - 2) = 15 - (x - 5) using a step-by-step approach. This lesson covers key algebraic concepts, suitable for students in Grades 7-9.

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