Question 1: Translate the phrase "Five more than twice a number" into an algebraic expression.

Answer: 2x + 5

Question 2: A rectangle has a length of 3 meters more than its width. Write an expression for its perimeter, using w for width.

Answer: Perimeter = 2(w + (w + 3))

Question 3: Identify and correct the mistake in this expression: "The sum of a number and 8 is 15, so the expression is n + 8 = 15."

Answer: The expression should be n + 8, representing the sum, not an equation; the expression itself is n + 8.

Question 4: A store sells apples at $2 each plus a fixed fee of $5 for delivery. Write an expression for the total cost, c, for buying x apples.

Answer: c = 2x + 5

Question 5: Plot the graph of y = 3x + 2 on the grid. Draw the line passing through points where x=0 and x=2.

Answer:

Question 6: Construct an expression for the total cost, in dollars, of buying x notebooks if each notebook costs $4 and there is a one-time shipping fee of $7.

Answer: Total cost = 4x + 7

Question 7: A cyclist pedals at a speed of 15 miles per hour plus an additional 2 miles per hour for every extra hour of rest taken. Write an expression for total distance after r hours of rest.

Answer: Distance = (15 + 2r) * total hours

Question 8: A gardener plants a certain number of trees. Each tree requires 3 liters of water, but she overestimates by 2 liters per tree. Write an expression for the total water needed.

Answer: Total water = 3n + 2

Question 9: Identify the error in this misconception: "Because the cost of x items is 5x, the total cost is always 5 times the number of items."

Answer: This is correct for linear cost without fixed fees; no error exists in the expression 5x.

Question 10: A recipe calls for 2 cups of sugar for every 5 cups of flour. Write an expression for the amount of sugar needed if you use x cups of flour.

Answer: Sugar = (2/5) x

Question 11: A phone plan charges a base fee of $20 plus $0.10 per minute of calls. Write an expression for the total cost, t, for x minutes of calls.

Answer: t = 20 + 0.10x

Question 12: A student notices that multiplying the number of pages read by 3 gives a certain total. She mistakenly thinks the total cost for printing pages is 3 times the number of pages. Explain the misconception and correct it.

Answer: The total printing cost depends on the cost per page, which may not be exactly 3 times the number of pages; the misconception is equating multiplication of pages with total cost without knowing the per-page fee.