Question 1: Rearrange the formula for the height of a wall: h = 2l + x, to make x the subject.

Answer: x = h - 2l

Question 2: If the length of a beam is given by L = 3x + 5, find x when L = 20.

Answer: x = 5

Question 3: In a window design, the width w is related to the height h by the formula: h = 4w + x. Rearrange to solve for x.

Answer: x = h - 4w

Question 4: Calculate x if the total perimeter P of a rectangular room is 60 meters, with length l and width w, using the formula: P = 2l + 2w + x, and the known values l = 15, w = 10.

Answer: x = 20

Question 5: In the context of designing a support beam, the formula is given by S = kx + c, where S is strength, x is the variable, k and c are constants. Rearrange to make x the subject.

Answer: x = (S - c) / k

Question 6: A contractor uses the formula for the volume of a rectangular prism: V = l * w * x. Rearrange to make x the subject.

Answer: x = V / (l * w)

Question 7: A designer is calculating the slope of a roof using the formula: slope = (rise) / (run) = x. Rearrange to solve for x.

Answer: x = slope * run

Question 8: A building's floor area A is given by A = x * y, where x is the length and y is the width. Rearrange to find x if A and y are known.

Answer: x = A / y

Question 9: In the design of a staircase, the formula relates the rise and run by: rise = kx + m. Rearrange to make x the subject.

Answer: x = (rise - m) / k

Question 10: A blueprint includes a formula for the length of an arch: L = 5x + 10. Find x when the length L is 40.

Answer: x = 6

Question 11: A roofing slope formula relates the height h to the horizontal distance d: h = m * d + x. Rearrange to make x the subject.

Answer: x = h - m * d

Question 12: Common mistake: A student rearranges h = 2l + x to x = h + 2l. Identify the error and correct it.

Answer: The correct rearrangement is x = h - 2l.