Question 1: Simplify the expression: 3x + 2x + 5

Answer: 5x + 5

Question 2: Simplify: 4a - 2a + a

Answer: 3a

Question 3: Simplify: 6m + 3m - m

Answer: 8m

Question 4: Simplify: 2y + y + y

Answer: 4y

Question 1: Explain why combining like terms is valid when simplifying algebraic expressions.

Answer: Because like terms have the same variable raised to the same power, allowing their coefficients to be added or subtracted.

Question 2: If 2x + 3x = 10, find the value of x.

Answer: x = 2

Question 3: Simplify: 7a - 2a + 4a - a

Answer: 8a

Question 4: A student simplifies 5b + 2b - 3b + b. What mistake might they make? How should it be correctly simplified?

Answer: They might forget to combine all like terms properly; correct simplification is 5b + 2b - 3b + b = 5b + 2b + b - 3b = 5b + 3b - 3b = 5b.

Question 1: A bakery sells cookies and muffins. If the total weight of 2 cookies and 3 muffins is 500 grams, and the weight of one cookie is represented by c grams, write an expression for the total weight in terms of c and simplify if possible.

Answer: 2c + 3m (cannot simplify further without muffin weight)

Question 2: A gardener combines 3 bags of soil weighing s kg each and 2 bags of fertilizer weighing f kg each. Write and simplify an expression for the total weight.

Answer: 3s + 2f

Question 1: Simplify: (x + 2) + (x - 3) + (2x + 1).

Answer: 5x - 0 = 5x

Question 2: Express the sum of the expressions 2a + 3b and a - 4b in simplest form.

Answer: 3a - b

Question 1: A student simplifies 4x + 3x - 2x + x as 6x. Is this correct? If not, what is the correct simplification?

Answer: Incorrect. The correct simplification is 4x + 3x - 2x + x = (4x + 3x + x) - 2x = 8x - 2x = 6x, so the student is correct.

Question 2: Identify and correct the mistake: Simplify 5m + 2n + 3m to 8m.

Answer: They incorrectly combined 5m and 3m as 8m without considering the term 2n. The correct expression is 8m + 2n.