Question 1: Write an algebraic expression for: 'Five more than twice a number.'

Answer: 2x + 5

Question 2: Translate: 'The sum of a number and seven.'

Answer: x + 7

Question 3: Express: 'Three times a number minus four.'

Answer: 3x - 4

Question 4: Construct an algebraic expression for: 'A number divided by six.'

Answer: x/6

Question 5: Translate: 'The product of a number and eight.'

Answer: 8x

Question 6: Write an expression for: 'The difference between twice a number and ten.'

Answer: 2x - 10

Question 7: If 'y' is twice 'x' plus three, write an expression for 'y'.

Answer: 2x + 3

Question 8: A rectangle's length is 'x + 4' and width is 'x - 2'. Write an expression for its perimeter.

Answer: 2(x + 4) + 2(x - 2) = 4x + 8 + 2x - 4 = 6x + 4

Question 9: Solve for 'x': 'Six less than three times a number equals 15.'

Answer: 3x - 6 = 15 => 3x = 21 => x = 7

Question 10: Express 'A number decreased by twice another number' in algebraic form.

Answer: x - 2y

Question 11: A student thinks of a number 'x'. They add 12 to it, then triple the result. Write this as an algebraic expression.

Answer: 3(x + 12)

Question 12: A factory produces 'n' units daily. If production increases by 10 units each day, write an expression for units produced on day 'd', assuming day 1's production is 'n'.

Answer: n + 10(d - 1)

Question 13: Identify and correct the mistake in the expression: '5x + 3 = 5(x + 3)'.

Answer: Incorrect; the expansion of 5(x + 3) is 5x + 15, so the original equation is not balanced. To correct, either change the right side to 5x + 15 or the left side to match.