I see the image you’ve uploaded contains a series of math problems. Let me extract the information and solve the problems for you. I'll provide the solutions with detailed steps below.

Section A: Problem 1

Write the number that should go in the empty box:

a. $(3 \times \_\_) + 4 = 19$
$(3 \times x) + 4 = 19$

1. Subtract 4 from both sides: $3 \times x = 15$
2. Divide by 3: $x = 5$ Answer: 5

b. $(6 \times \_\_) + 1 = 25$
$(6 \times x) + 1 = 25$

1. Subtract 1 from both sides: $6 \times x = 24$
2. Divide by 6: $x = 4$ Answer: 4

c. $(\_\_ \times 5) - 1 = 19$
$(x \times 5) - 1 = 19$

1. Add 1 to both sides: $x \times 5 = 20$
2. Divide by 5: $x = 4$ Answer: 4

d. $(8 \times 6) - \_\_ = 45$
$(8 \times 6) - x = 45$

1. Calculate $8 \times 6$: $48 - x = 45$
2. Subtract 45 from 48: $x = 3$ Answer: 3

e. $(9 \times 9) + \_\_ = 83$
$(9 \times 9) + x = 83$

1. Calculate $9 \times 9$: $81 + x = 83$
2. Subtract 81 from 83: $x = 2$ Answer: 2

Section A: Problem 2

Write the number that should go in the empty box:

a. $(\_\_ \times 3) + 2 = 23$
$(x \times 3) + 2 = 23$

1. Subtract 2 from both sides: $x \times 3 = 21$
2. Divide by 3: $x = 7$ Answer: 7

b. $(\_\_ \times 4) + 4 = 29$
$(x \times 4) + 4 = 29$

1. Subtract 4 from both sides: $x \times 4 = 25$
2. Divide by 4: $x = 6.25$ Answer: 6.25

c. $(\_\_ + 1) = 64$
$x + 1 = 64$

1. Subtract 1 from both sides: $x = 63$ Answer: 63

d. $(\_\_ + \_\_) - 1 = 15$
Here, we have two variables. Let’s assign them as $a$ and $b$: $a + b - 1 = 15$

1. Add 1 to both sides: $a + b = 16$ This problem requires additional information to solve further. Possible combinations of $a$ and $b$ include:
   • $a = 8, b = 8$
   • $a = 10, b = 6$, etc.

e. $(\_\_ + \_\_) - 10 = 26$
Assign $a$ and $b$: $a + b - 10 = 26$

1. Add 10 to both sides: $a + b = 36$ This problem requires additional information to solve further. Possible combinations of $a$ and $b$ include:
   • $a = 18, b = 18$
   • $a = 20, b = 16$, etc.

Let me know if you'd like any step clarified further or help with the undetermined variables!

5 Questions to Expand Understanding:

1. How can you verify your solutions for equations involving multiple variables?
2. What strategies can you use for guessing pairs of numbers in problems like 2(d) and 2(e)?
3. Why is it important to perform inverse operations when solving equations?
4. How can these equations relate to real-life problem-solving scenarios?
5. What are the different methods to solve equations with fractions or decimals?

One Tip:

Always double-check your solution by substituting it back into the original equation to ensure it works perfectly!